Homework Progress
0
Find the nth term of the following sequence: 4 7 12 19 28
Answers
Answer:
n²+3
Explanation:
The differences between the terms are not the same, so this is not "linear". Knowing that the sequence may have started with a 1, you can try subtracting the first number with a number to get 1, and use that number to subtract the rest.
4 - 3 = 1
7 - 3 = 4
12 - 3 = 9
19 - 3 = 16
28 - 3 = 25
In this case, subtracting 3 to all the numbers gave us perfect squares! So this means the nth term has to do with squaring the number and adding three afterward! This can be checked.
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
As we found the values of these terms by subtracting three first and then finding its square root, the nth term will be the opposite; squaring and then adding three! Again, this can be checked!
1² + 3 = 4
2² + 3 = 7
3² + 3 = 12
4² + 3 = 19
5² + 3 = 28
Hope this helps !! :D
Related Questions
how to find slant height of a pyramid
Answers
Answer:
To find the slant height of a pyramid, you need to know the length of the base and the height of the pyramid The slant height can be found using the Pythagorean theorem, which states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the slant height of a pyramid is:
Slant height = √ (Base² + Height²)
For example, if the base of a is 10 meters and the height is 20 meters, then the slant height is:
Slant height = √ (10² + 20²) = √500 = 10√5 meters
Answer: We can find slant height of pyramid by using pythagorean theorem which states that (height)^2 + (half lateral edge length)^2 = (slant height)^2.
Step-by-step explanation:
To find the slant height of pyramid we need to know the height of the pyramid and the lateral edge length.
The height of the pyramid is the perpendicular distance from the base to the apex. The lateral edges are the edges that connect apex to the vertices of the base.
Applying pythagorean theorem, we can calculate the slant height of the pyramid by using the formula-
(slant height)^2 = (height)^2 + (half lateral edge length)^2
or simply we can write as: \(s= \sqrt{h^{2} + (l/2)^{2}\).
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find the missing value to complete the square.
x^2 +8x+ ___
Answers
Answer:
the answer is x^2+8x+ c
Step-by-step explanation:
If x 2 + b x + c is a perfect square, then there is always the same relation ship between b and c "Find half of b and square it" , so c = ( b /2 ) ^2
x^ 2 + 8 x + ( 8/ 2 )^2 =
x^ 2 + 8 x + 4^ 2 =
x^ 2 + 8 x + 16 =
( x + 4 ) ^2
I hope that helps you
YJHW1 20. search eBook Problem 7-20 Nonconstant Growth Stock Valuation Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 15% annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and RT's growth rate will slow to 3% per year indefinitely Stockholders require a return of 12% on RT's stock. The most recent annual dividend (Di), which was paid yesterday, was $1.95 per share.a. Calculate RT's expected dividends for t= 1.t= 2, tad answers to the nearest cent D₁ = 2.24 D₂ = 2.58 D₃ = 2.97D₄ = 3.41 D₅ = 3.92 b. Calculate the estimated intrinsic value of the stock today, P₀, Proceed by finding the present value of the dividends expected at t-1.1-2, 1-3,1-4, and t5 plus the present value of the stock price that should exist at t = ≤. P₂. The P₂, stock price can be found by using the constant growth equation. Note that to find P₂ you use the dividend expected atte, which is greater than the t = 5 dividend. Round your answer to the nearest cent. Do not round your intermediate computations c. Calculate the expected dividend yield (D₁/ P₀ ), the capital gains yield expected during the first year, and the expected total return (dividend yield plus capital gains yield) during the first year. (Assume that P₀ = ₚ₀ , and recognize that the capital gains yield is equal to the total return minus the dividend yield.). Round your answers to two decimal places. Do not round your intermediate computations. Expected dividend yield: Capital gains yield Expected total return Also calculate these same three yields for t = 5 (e.g., D₁ Pₛ). Round your answers to two decimal places. Do not round your intermediate computations. Expected dividend yield Capital gains yield Expected total return
Answers
a. The expected dividends for t = 1 to t = 5 are as follows:
D₁ = $2.24
D₂ = $2.58
D₃ = $2.97
D₄ = $3.41
D₅ = $3.92
b. To calculate the estimated intrinsic value of the stock today (P₀), we need to find the present value of the dividends expected at t = 1 to t = 5 and the present value of the stock price at t = 5. Using the constant growth equation, we find:
P₂ = D₆ / (r - g) = D₅ * (1 + g) / (r - g) = $3.92 * (1 + 0.03) / (0.12 - 0.03) = $53.52
Now, we can find the present value of the dividends and the stock price:
P₀ = D₁ / (1 + r) + D₂ / (1 + r)² + D₃ / (1 + r)³ + D₄ / (1 + r)⁴ + D₅ / (1 + r)⁵ + P₂ / (1 + r)⁵
= $2.24 / (1 + 0.12) + $2.58 / (1 + 0.12)² + $2.97 / (1 + 0.12)³ + $3.41 / (1 + 0.12)⁴ + $3.92 / (1 + 0.12)⁵ + $53.52 / (1 + 0.12)⁵
= $2.00 + $2.14 + $2.17 + $2.04 + $2.07 + $33.48
= $43.90
c. For the first year (t = 1), we can calculate the expected dividend yield (D₁ / P₀), the capital gains yield (expected total return minus the dividend yield), and the expected total return as follows:
Expected dividend yield = D₁ / P₀ = $2.24 / $43.90 = 0.051 (or 5.1%)
Capital gains yield = Expected total return - Expected dividend yield = 0.12 - 0.051 = 0.069 (or 6.9%)
Expected total return = Expected dividend yield + Capital gains yield = 0.051 + 0.069 = 0.12 (or 12.0%)
For t = 5:
Expected dividend yield = D₅ / P₀ = $3.92 / $43.90 = 0.089 (or 8.9%)
Capital gains yield = Expected total return - Expected dividend yield = 0.03 - 0.089 = -0.059 (or -5.9%)
Expected total return = Expected dividend yield + Capital gains yield = 0.089 - 0.059 = 0.03 (or 3.0%)
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A. 9,10 B.10,8.3 C. -10,8.3 D-9,10
Answers
This question makes an important point: the maximum point of a function may not always be found by solving f'(x) = 0 Remember: functions can have their minimum or maximum at an endpoint of their domain, at a point of non-differentiability (think of the absolute value function, which has its minimum point at zero) or may not even have a maximum or minimum. This means that the most thorough way of solving optimization problems involves sketching the objective function. (For questions that appear on tests, however, the optimum will usually occur at a relative max. or relative min. that can be found by solving f'(x) = 0.) Two parts of this question are multiple choice: you only get one submission attempt for those two parts. A peach orchard owner wants to maximize the amount of peaches produced by his orchard. He has found that the per-tree yield is equal to 900 whenever he plants 30 or fewer trees per acre, and that when more than 30 trees are planted per acre, the per-tree yield decreases by 40 peaches per tree for every extra tree planted. For example, if there were 25 trees planted per acre, each tree would produce 900 peaches. If there were 35 trees planted per acre, each tree would produce 900 - 40 (35 - 30) peaches, which is roughly equal to 700 peaches. Find the function that describes the per-tree yield, Y, in terms of x. Y = if is no more than 30 trees per acre Y= Find the total yield per acre, T, that results from planting x trees per acre. T = if is no more than 30 trees per acre T = | c. Differentiate T with respect to x dT/dx = dT/dx = Does this derivative ever equal zero? Yes No d. Sketch the graph of T as x varies and hence find the value of x that maximizes the yield and the maximum value of the yield. Optimal value of : trees per acre Maximum yield : peaches per acre Is T differentiable when Times equals 30? Yes No
Answers
The maximum point of a function found by solving f'(x) = 0
1.Y(x) = 900, if x ≤ 30
2.900 - 40(x - 30), if x > 30
3.T(x) = x × Y(x)
4.dT/dx = 900, if x < 30
5.2100x - 40x² if x > 30
6.The derivative dT/dx equals zero at x = 52.5, but it is not valid in the given context.
7.The maximum yield occurs at x = 30 trees per acre, with a maximum yield of 27,000 peaches per acre.
8.T(x) is differentiable at x = 30.
To find the function that describes the per-tree yield, Y, in terms of x, use the given information:
If there are 30 or fewer trees planted per acre (x ≤ 30), the per-tree yield is 900 peaches per tree.
If there are more than 30 trees planted per acre (x > 30), the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30.
The function Y(x) as follows:
Y(x) = 900, if x ≤ 30
Y(x) = 900 - 40(x - 30), if x > 30
find the total yield per acre, T, that results from planting x trees per acre. The total yield is simply the per-tree yield (Y) multiplied by the number of trees per acre (x):
T(x) = x × Y(x)
differentiate T with respect to x (dT/dx) to find where the maximum yield occurs.
dT/dx = d/dx (x × Y(x))
dT/dx = d/dx (x × (900 - 40(x - 30)))
To find if this derivative ever equals zero, it to zero and solve for x:
0 = 900 - 40(x - 30)
40(x - 30) = 900
x - 30 = 22.5
x = 52.5
So, the derivative dT/dx equals zero at x = 52.5. However, we need to check whether this value is valid for our function. Recall that if x > 30, the per-tree yield decreases by 40 peaches for every extra tree planted beyond 30. Therefore, planting 52.5 trees per acre would result in a negative per-tree yield, which is not physically meaningful in this context. Thus, the maximum yield occurs at the critical point within the valid domain, which is x = 30.
Now, let's find the maximum value of the yield at x = 30:
T(30) = 30 ×Y(30) = 30 × 900 = 27,000 peaches per acre
The optimal value of x that maximizes the yield is 30 trees per acre, and the maximum yield is 27,000 peaches per acre.
Finally, let's determine if T(x) is differentiable when x equals 30. Since T(x) is a piecewise function, we need to check if the left and right-hand derivatives at x = 30 are the same.
Left-hand derivative (x < 30):
dT/dx = d/dx (x × 900) = 900
Right-hand derivative (x > 30):
dT/dx = d/dx (x × (900 - 40(x - 30))) = d/dx (x × (900 - 40x + 1200)) = d/dx (2100x - 40x²)
Now, evaluate the right-hand derivative at x = 30:
dT/dx = 2100(30) - 40(30)² = 63,000 - 36,000 = 27,000
Since the left-hand derivative and the right-hand derivative at x = 30 are equal (both are 27,000), T(x) is differentiable at x = 30.
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Solve the right triangle ABC, with C=90°. B=36°12′ c=0.6209 m
Answers
In triangle ABC, we are given that angle C is a right angle, which means it measures 90°. We also know that angle B is 36°12′, and side c has a length of 0.6209 m. Our goal is to find the measures of angle A and the lengths of sides a and b.
Using the fact that the sum of angles in a triangle is 180°, we can find angle A:
A + B + C = 180°
A = 180° - B - C = 180° - 36°12′ - 90° = 53°48′
Now, we can apply the trigonometric ratios in the right-angled triangle ABC. The ratios are defined as follows:
Sine (sin) = Opposite / Hypotenuse
Cosine (cos) = Adjacent / Hypotenuse
Tangent (tan) = Opposite / Adjacent
Using the given values, we can determine the lengths of sides a and b:
Sine ratio:
sin B = a / c
Substituting the known values, we find:
sin 36°12′ = a / 0.6209
a = 0.6209 x sin 36°12′ = 0.3774 m
Cosine ratio:
cos B = b / c
Substituting the known values, we find:
cos 36°12′ = b / 0.6209
b = 0.6209 x cos 36°12′ = 0.5039 m
Tangent ratio:
tan B = a / b
Substituting the values of a and b, we find:
tan 36°12′ = 0.3774 / 0.5039 = 0.7499
Therefore, the lengths of sides a and b are approximately 0.3774 m and 0.5039 m, respectively. Angle A measures 53°48′, angle B measures 36°12′, and angle C is the right angle.
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HI PLEASE ANSWER THIS QUESTION THANK YOU!
(NO TROLLS PLEASE!)
Answers
T/F: Nonsampling errors reduce the overall quality of data regardless of the data collection method.
Answers
True. Nonsampling errors refer to errors that occur during the data collection process that are not related to the sampling method used. These errors can occur in any type of data collection method, whether it be through surveys, experiments, or observational studies.
Nonsampling errors can arise due to a variety of reasons, such as poor survey design, biased sampling methods, inadequate training of surveyors, errors in data entry or processing, or even deliberate fraud.
Nonsampling errors can have a significant impact on the quality of the data collected, as they can introduce biases and inaccuracies into the results. These errors can result in incorrect conclusions and decisions based on the data, which can have serious consequences. Therefore, it is important to take steps to minimize nonsampling errors during the data collection process, such as carefully designing surveys, ensuring proper training of surveyors, and conducting thorough quality checks on the data collected.
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pla shop mathematics
Answers
The number of trees more than 10m tall but not more than 20m tall is 18 trees.
How many of the trees are more than 10m tall but not more than 20m tall?0 < h ≤ 5 = 5
height greater than 0m less than or equal to 5m
5 < h ≤ 10 = 9
height greater than 5m less than or equal to 10m
10 < h ≤ 15 = 13
height greater than 10m less than or equal to 15m
15 < h ≤ 20 = 5
height greater than 15m less than or equal to 20m
20 < h ≤ 25 = 1
height greater than 20m less than or equal to 25m
The number of trees that are more than 10m tall but not more than 20m tall are;
10 < h ≤ 15 = 13
15 < h ≤ 20 = 5
So,
13 + 5 = 18 trees
Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.
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Can't figure this out please help
Answers
In quadrilateral ABCD m ZA-90° m / C = 50° and m B = m 2D. Find the degree measure of Z B.
Answers
The sum of the internal angles in a quadrilateral is equal to 360, therefore:
\(\begin{gathered} \angle A+\angle B+\angle C+\angle D=360 \\ 90+\angle B+50+\angle B=360 \\ 140+2\angle B=360 \\ 2\angle B=360-140 \\ 2\angle B=220 \\ \angle B=\frac{220}{2} \\ \angle B=110 \end{gathered}\)A pack of snack bars includes 2 blueberry bars , 3 chocolate bars , and 5 cherry bars . What is the ratio of the number of blueberry bars to the number of cherry bars ?
Answers
Answer:
2:5 is the ratio in this situations
Step-by-step explanation:
There are 2 blueberry bars, and 5 cherry.
Is x=8 a solution to the inequality below? Justify your yes/no answer. -2x+10>x-6
Answers
Answer: no
Step-by-step explanation:
Answer: no
-2x + 10 > x - 6
⇔ x + 2x < 10 + 6
⇔3x < 16
⇔ x < 16/3
⇔ x < 5.3
=> x = 8 isnt a solution
Step-by-step explanation:
Jenny solved the equation 1 – (2x + 4) = –4x + 5. Her work is shown. 1 − ( 2 x + 4 ) = − 4 x + 5 Line 1: 1 − 2 x + 4 = − 4 x + 5 Line 2: 5 − 2 x = − 4 x + 5 Line 3: 2 x = 0 Line 4: x = 0 What is the correct solution to the equation 1 – (2x + 4) = –4x + 5? Re-solve the equation to find the correct solution.
Answers
Answer:
4Step-by-step explanation:
Given the equation 1 – (2x + 4) = –4x + 5, we are to find the correct solution of the equation;
Step 1: Open the parenthesis;
1 – (2x + 4) = –4x + 5
1-2x-4 = -4x + 5
1-4-2x = -4x +5
-3-2x = -4x + 5
Step 2: Collect like terms
-2x + 4x = 5 + 3
2x = 8
Step 3: divide both sides by 2;
2x/2 = 8/2
x = 4
Hence the correct value of x is 4
if you create an online survey, individuals can choose on their own whether to participate in the sample. this causes a form of bias called __________.
a. voluntary response
b. undercoverage
c. response
d. non-response
Answers
The correct answer is a. voluntary response.
Voluntary response bias occurs when individuals have the freedom to choose whether or not to participate in a sample or survey. In such cases, participation is entirely voluntary, and individuals self-select themselves into the sample. This type of bias can lead to misleading or unrepresentative results.
Voluntary response bias is a concern because it can introduce systematic differences between those who choose to participate and those who do not. Individuals who have strong opinions or a vested interest in the topic of the survey are more likely to participate, while those who are indifferent or have no strong opinion may opt out. As a result, the sample may overrepresent certain viewpoints or groups while underrepresenting others.
This bias can lead to skewed results that do not accurately reflect the larger population. The opinions and characteristics of the individuals who choose to participate may not be representative of the broader population, making it challenging to generalize the findings.
To mitigate voluntary response bias, it is important to use random sampling methods where participants are selected randomly from the target population. This helps ensure that all individuals have an equal chance of being included in the sample, providing a more representative and unbiased view of the population.
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the probability of drawing two nickels from a bag at random without replacement is 3395. the probability of drawing a nickel first is 35. what is the probability of drawing a second nickel, given that the first coin drawn was nickel?
Answers
The probability of drawing a second nickel, given that the first coin drawn was nickel is 11/19
Given that the probability of drawing two nickels from a bag at random without replacement is 33/95, and the probability of drawing a nickel first is 3/5
Then, the probability of two events happening is equal to the product of the probabilities of each event occurring.
For this item, we can let x be the unknown probability to established a relationship between them as follows:
(3/5)*(x)=33/95
x=33/95*5/3
x=11/19
The value of x from the equation is 11/19. Thus, the probability of drawing a second nickel, given that the first coin drawn was nickel is 11/19
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Balloons are filled to capacity outdoors where the temperature is 25∘F. They are brought indoors where the temperature is 70∘F. Explain what will happen to the balloons as they warm up indoors.
Answers
When balloons filled to capacity outdoors at a temperature of 25∘F are brought indoors where the temperature is 70∘F, they will expand and increase in size as they warm up. The increase in temperature causes the air molecules inside the balloons to gain energy and move more rapidly.
When the balloons are brought indoors where the temperature is 70∘F, the air inside the balloons will begin to warm up. As the temperature increases, the air molecules inside the balloons gain energy and start to move more rapidly. This increased movement of the air molecules causes them to collide with the walls of the balloons more frequently and with greater force.
The collision of the air molecules with the walls of the balloons creates pressure inside the balloons. As the pressure increases, the balloons will start to expand and stretch. This expansion occurs because the rubber material of the balloons is flexible and can accommodate the increased volume of air.
As the balloons continue to warm up, the expansion will become more noticeable. The balloons will increase in size and become tauter. This happens because the air molecules inside the balloons are now occupying a larger space due to the increase in temperature. The rubber material of the balloons stretches to accommodate the greater volume of air.
It's important to note that if the temperature difference is significant, the expanding balloons may eventually reach their limits and could potentially burst if they are unable to withstand the internal pressure. Therefore, it's crucial to consider the temperature conditions when filling balloons to avoid overinflation.
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see attached photo, please help asap!!!
Answers
Answer:
3.398
Step-by-step explanation:
log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398
Which hypothesis should be written as an inequality? A. the null hypothesis B. the alternative hypothesis C. either the alternative or the null hypothesis
Answers
The hypothesis that should be written as an inequality is B. the alternative hypothesis.
The alternative hypothesis is a statement that contradicts the null hypothesis and is used to determine if there is a significant difference between two variables. It is often written as an inequality to show that there is a difference between the two variables being tested.
For example, if we are testing whether a new drug is more effective than a placebo, the alternative hypothesis would be written as "the new drug is more effective than the placebo," or in inequality form, "the effectiveness of the new drug > the effectiveness of the placebo."
In contrast, the null hypothesis is a statement that there is no significant difference between the two variables being tested. It is usually written as equality, such as "the new drug is equally effective as the placebo," or "the effectiveness of the new drug = the effectiveness of the placebo."
Therefore, the alternative hypothesis is the one that should be written as an inequality.
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if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
Answers
Yes , the confidence interval still valid because the sample size is large ( n = 100 is greater than 30 ).
Given :
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid .
Here
sample size n = 100
The sample size is a term used in market research for defining the number of subjects included in a sample size.
here
n > 30
Hence the confidence interval is still valid .
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Full question:
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
Answers
HHHH, 0 tails and 4 heads
HHHT, 1 tails and 3 heads
HHTH, 1 tails and 3 heads
HHTT, 2 tails and 2 heads
HTHH, 1 tails and 3 heads
HTHT, 2 tails and 2 heads
HTTH, 2 tails and 2 heads
HTTT, 3 tails and 1 heads
THHH, 1 tails and 3 heads
THHT, 2 tails and 2 heads
THTH, 2 tails and 2 heads
THTT, 3 tails and 1 heads
TTHH, 2 tails and 2 heads
TTHT, 3 tails and 1 heads
TTTH, 3 tails and 1 heads
TTTT, 4 tails and 0 heads
Eleven of these outcomes have a head-to-tail ratio of at least one head for every two tails. Therefore, there is an 11/16 chance of getting at least as many heads as tails.
Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given by the equation C 200 +2/3(Y- T). Planned investment is 300, as are government spending and taxes. a. If Yis 1,500, what is planned spending? What is inventory accumulation or decumulation? Should equilibrium Ybe higher or lower than 1,500? b. What is equilibrium Y? (Hint: Substitute the values of equations for planned consumption, investment, and government spending into the equation Y-C++ G and then solve for Y.) c. What are equilibrium consumption? d. How much does equilibrium income decrease when G is reduced to 200? what is the multiplier for government spending?
Answers
The mean value of the given data set is 31.333. To find the mean value of the given data set (10, 10, 20, 26, 30, X), we first need to determine the missing value, denoted as X, using the given range of 40.
Since the range is the difference between the maximum and minimum values, we can set up the equation:
Maximum value - Minimum value = Range
X - 10 = 40
Solving for X, we find X = 50.
Now that we have the complete data set (10, 10, 20, 26, 30, 50), we can calculate the mean. Summing up all the values and dividing by the total number of values (6), we find the mean to be 31.333 (rounded to three decimal places).
In conclusion, the mean value of the given data set is 31.333.
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Amelia is making a cookie recipe that requires 4 cups of sugar for every 12 cups of flour. Amelia only has 9 cups of flour. She concludes that she will only need 3 cups of sugar Is Amelia correct? Why or why not?
A Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12.
B Amelia is correct. One-quarter the amount of sugar is needed because only one-quarter of the recipe will be made.
C Amelia is incorrect. The number of cups of sugar must be reduced by 3 because the number of cups of flour is reduced by 3.
D Amelia is incorrect. She needs 4 cups of sugar because decreasing the number of cups of flour by 3 requires increasing the number of cups of sugar by 3.
Answers
Answer:
B
Step-by-step explanation:
Because if you will divide the ratio 4:12 by three- we will get a ratio 1:3. Then we need the last 3 in the ratio 1:3 become a 9. For this we need to multiply it by 3= 1:3 *3= 3:9. This is only 3/4 of whole of recipe.
Answer: Choice A)
Amelia is correct. She needs 3 cups of sugar because the ratio 3:9 is equivalent to 4:12
=======================================================
Explanation:
It might help to think of the ratio 4:12 as the fraction 4/12. Dividing both parts by 4 leads to 1/3.
Similarly, the ratio 3:9 becomes 3/9 which reduces to 1/3.
This shows that 4/12 = 3/9, so the ratios 4:12 and 3:9 are the same.
------------
Another way to show two fractions are equal is to do the steps below
4/12 = 3/9
4*9 = 12*3 ... cross multiply
36 = 36
Since the last equation is true, the first equation must be true.
-------------
Here's another way to see Amelia is correct.
So we know that 4 cups of sugar go with 12 cups of flour. This forms the fraction 4/12.
We also know that she has 9 cups of flour. Let's say we don't know how much sugar she needs, so we'll call this x. We have x cups of sugar go with 9 cups of flour. This forms the fraction x/9.
Equate the two fractions and solve for x
4/12 = x/9
9*4 = 12*x ... cross multiply
36 = 12x
12x = 36
x = 36/12 ... divide both sides by 12
x = 3
She needs 3 cups of sugar
The steps in this section are very similar to the steps in the last section.
A 12 -foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?
Answers
The height of the wall where the ladder reaches will be 6.33 feet.
What is a Pythagoras theorem?It communicates that the area of the square whose side is the hypotenuse is identical to how much the locale of the squares on the other various sides.
The Pythagoras theorem formula is given as
H² = P² + B²
A 12-foot ladder is set against a vertical mass of construction, with the lower portion of the ladder staying on level ground 10 feet from the underpinning of the design.
The height of the wall where the ladder reaches will be calculated as,
12² = P² + 10²
144 = P² + 100
P² = 44
P =6.33 feet
The level of the wall where the stepping stool arrives freely will be 6.33 feet.
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0.738×0.28 is 0.20664 but is rounded to 0.21. which rule or rules are applied to this calculation? select all that apply.
Answers
The rules of the calculation are:
Round the result to the same number of significant figures as the value with the least number of significant figuresRound up if the digit to be dropped is 5 or greater.How to determine the rule?The complete question is added as an attachment
The equation is given as:
0.738 × 0.28 = 0.20664
When approximated, we have:
0.738 × 0.28 ≈ 0.21
The above approximation can mean any of the following:
To 2 decimal placesTo the nearest hundredthTo 2 significant digitsRead more about approximation at:
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What is the equation for the line through the origin and (3, 4)
Answers
Answer:
y = (4/3)x
Step-by-step explanation:
We can use y = mx + b where b is the y-intercept and m is the slope. We can see that the slope is (4-0)/(3-0) = 4/3 and the y-intercept is at (0,0). Thus, m = 4/3 and b = 0. Substituing that in, we get that the equation is y = (4/3)x.
I hope this helps! :)
work out 5^-2 x cube root 8
Answers
Answer:
0.08
Step-by-step explanation:
5 ^-2 * cube root of 8
first of all, let us solve 5^-2
using the law of indices;
a^-2 = 1 / a ^2
following this law, we have;
5^-2 = 1 / 5^2
we know that 5^2 = 25
therefore,
5^-2 = 1 / 25
now, let is continue by solving the cube root of 8
now, there are three ways of solving this;
we could just simply think of any number that when multiplies itself three times times, it gives 8, or we could just simply use a calculator
regardless of what we use, we have to end up with the number 2 as the answer
leading is to our conclusion.
from all our solution, we have reduced our question to;
1 / 25 ( which is 5^-2) * 2 ( which is the cube root of 8 )
= 1 / 25 * 2 / 1
note that 2 is the same as 2 / 1. We put it like this when we want to carry out an operation on an integer ( e.g. 2) and and a fraction ( e.g. 1 / 25 )
so,
1 / 25 * 2 / 1 =
2 / 25 ( the two multiplies the 1 in 1 / 25 and the 25 multiplies the 1 in 2 / 1)
leaving our answer in decimal, we have;
0.08
hope this helps,
thanks!!!
___ A warm front brings warmer weather with light precipitation
A.true
B.false
Answers
BRAINLIEST PERSON WHO GETS IT
Nyoko wrote these two questions.
Equation 1: 6x-5+2x = 4(2x-1) - 1
Equation 2: 3x +7 = bx+7
Part A
Nyoko says that Equation 1 has one solution. Do you agree with her? Explain your reasonings.
Part B
Can Nyoko find a value for b in Equation 2 so that the equation has no solutions? Explain Your REASONING!
Answers
a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.
b) Nyoko cannot find a value of b so that the equation has no solutions.
How to solve the equations?The equation 1 is given as follows:
6x - 5 + 2x = 4(2x - 1) - 1.
Combining the like terms and applying the distributive property, the simplified equations are given as follows:
8x - 5 = 8x - 4 - 1
8x - 5 = 8x - 5.
As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.
The equation 2 is given as follows:
3x + 7 = bx + 7.
A system of linear equations will have zero solutions when:
The equations have the same slope.The equations have different intercepts.As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.
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an exponential function is expressed in the form y ab x the relation represents a growth when
Answers
Answer:
b > 1
Step-by-step explanation:
You want to know the conditions on an exponential function that represents growth.
Growth factorThe value of 'b' in the exponential function y = a·b^x is called the "growth factor." Each time x increases by 1 unit, the value of y is multiplied by 'b'. If that product is increasing, the value of 'b' must be greater than 1.
The relation represents growth when b > 1.
An exponential function in the form \(y = ab^x\) represents growth when the base (b) is greater than 1.
What is exponential function?In an exponential function of the form y = ab^x, the base (b) is a crucial component. The behavior of the function depends on the value of the base.
When the base (b) is greater than 1, it means that b is a positive number larger than 1. In this scenario, as the value of x increases, the value of \(b^x\) also increases exponentially. This results in the function \(y = ab^x\) exhibiting growth.
To better understand this growth behavior, let's consider an example. Suppose we have an exponential function \(y = 2^x\). As x increases from 0, the values of \(2^x\) will be as follows:
For x = 0, \(2^0\) = 1
For x = 1, \(2^1\) = 2
For x = 2, \(2^2\) = 4
For x = 3, \(2^3\) = 8
For x = 4, \(2^4\) = 16
As you can see, as x increases, the values of \(2^x\) grow exponentially. This demonstrates the growth behavior of exponential functions when the base is greater than 1.
It's important to note that when the base (b) is between 0 and 1 (exclusive), the exponential function will exhibit decay or decreasing behavior rather than growth.
In summary, an exponential function of the form \(y = ab^x\) represents growth when the base (b) is greater than 1. As x increases, the function values increase exponentially, indicating a growth pattern.
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