Problem 1
Answer: Choice C) -511---------------------------------------
Work Shown:
a1 = 9 = first termd = -7 = common differenceWe decrease by 7 each time we need a new term
an = nth term
an = a1+d(n-1)
an = 9+(-7)(n-1)
an = 9-7n+7
an = -7n+16
a14 = -7*14+16
a14 = -82
Sn = sum of the first n terms of an arithmetic sequence
Sn = (n/2)*(a1+an)
S14 = (14/2)*(9+(-82))
S14 = -511
================================================
Problem 2
Answer: Choice C) \(a_n = -6(a_{n-1}), \ a_1 = -2.5\)--------------------------------------
Explanation:
The nth term of a geometric sequence is a*r^(n-1)
a = first termr = common ratioWe're given that
a2 = 15 = second terma5 = -3240 = fifth termThose two facts lead us to these two equations
a*r = 15a*r^4 = -3240Divide the second equation over the first equation
The left hand sides would divide to r^3
The right hand sides divide to -216
Solving r^3 = -216 leads to r = -6
This leads to...
a*r = 15
a*(-6) = 15
a = 15/(-6)
a = -2.5
This points us at choice C as the answer. Choice C says that the nth term is found by multiplying the previous term by -6, which is tied directly to the common ratio.
What is the value of square root 30 is between witch two integers
A-4and5
B-5and6
C-6and7
D-7and8
Answer:
b
Step-by-step explanation:
because
What is the equation of a line that passes through (1,2) and is perpendicular to the given line?
The given line passes through (0,10) and (2,0), so its slope is
\(\frac{10-0}{0-2}=-5\)
Since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/5.
Substituting into point-slope form,
\(y-2=\frac{1}{5}(x-1)\\\\y-2=\frac{1}{5}x-\frac{1}{5}\\\\\boxed{y=\frac{1}{5}x+\frac{9}{5}}\)
Solve this system of equations
3x+3y+z =-18
x-3y+2z=15
8x-2y+3z=7
24 pieces of candy in 3 bags how much candy's per bag
the fastest man in the world can run 100 metres in 9 seconds how far can He run in 1 minute and 2 seconds
With steps plz......
(Its not usain)
Answer:
Step-by-step explanation:
Rate per sec = 100 ÷ 9 = 11.111
1 min and 2 sec = 3600 + 2sec = 3602 sec
Metre = 324.21 metre
Answer the following questions with TRUE or FALSE. It is good practice to explain your answers. (a) The intersection of two events A and B can be larger than the union of the same two events A and B (b) The probability of a single event A must be smaller than or equal to the union of two events A and B (c) The condition probability of A given B must be smaller than the intersection of the same two events A and B
a) The statement " The intersection of two events A and B can be larger than the union of the same two events A and B" is False.
b) The statement " The probability of a single event A must be smaller than or equal to the union of two events A and B" is False.
c) The statement " The condition probability of A given B must be smaller than the intersection of the same two events A and B" is False.
(a) False. The intersection of two events A and B represents the set of outcomes that are common to both A and B, while the union of the same two events A and B represents the set of outcomes that belong to either A or B or both. Hence, it cannot be larger than the union of A and B.
(b) False. The probability of an event A must be between 0 and 1 (inclusive), while the union of two events A and B represents the set of outcomes that belong to either A or B or both. The probability of the union of A and B is the sum of the probabilities of A and B, which can be larger than the probability of A.
(c) False. The conditional probability of A given B, denoted as P(A|B), represents the probability of event A occurring given that event B has already occurred. Since the intersection of A and B must be less than or equal to 1, the conditional probability of A given B must also be less than or equal to 1.
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A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
Work out the volume of the prism height of 12 4 and five
The calculated volume of the prism is 702 cubic cm
Finding the volume of the prismFrom the question, we have the following parameters that can be used in our computation
The trapezoidal prism (see attachment)
The formula of the volume of a trapezoidal prism is
Volume = Base area * Height
Where we have
Base area = 1/2 * (8 + 10) * 6
Evaluate the sum of 8 and 10
Base area = 1/2 * 18 * 6
Evaluate the products of 1/2, 18 and 6
Base area = 54
Also, we have
Height = 13
So, the volume is calculated as
volume = 13 * 54
Evaluate
volume = 702
Hence, the volume of the prism is 702 cubic cm
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HELPPP!!!
Create a residual plot for your data.
A residual plot is a scatterplot in which the residuals (vertical distances between the predicted and actual values) are plotted against the independent variable. A residual is defined as the difference between the predicted value (based on the regression equation) and the actual value.
Residual plots are a valuable tool for checking the adequacy of the model. It helps us check whether the assumptions of linearity, independence, equal variance, and normality are met or not.
The most basic way to create a residual plot is to plot the residuals against the fitted values. If the points in the residual plot are randomly scattered around the horizontal axis, then the assumption of linearity has been met.
If the points show a pattern, such as a curved line, then the assumption of linearity has been violated.To create a residual plot, follow these steps:
Step 1: Estimate the regression equation and obtain the predicted values (ŷ) and residuals (e). ŷ = b0 + b1X
Step 2: Plot the residuals on the vertical axis and the independent variable (X) on the horizontal axis
.Step 3: Look for patterns in the residual plot. If the points are randomly scattered around the horizontal axis, then the assumptions of linearity, independence, equal variance, and normality are met. If there is a pattern, such as a curved line, then the assumptions have been violated. A residual plot can be used to detect outliers, influential observations, and nonlinearity.
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15,20,15,30,25 median mean mode
Answer:
Median:20
mean:21
mode:15
Hello there! :)
To find the mean, we must add all the terms in the dataset and then divide by how many there are.
15+20+15+30+25=105
105÷5=21
So the mean is 21.
To find the median, we must find the number in the middle.
First, arrange the terms from least to greatest:
15, 15, 20, 25, 30
Now, we can see than 20 is the median.
To find the mode, we must find the number that is seen most often in the dataset.
15 is seen twice
20 is seen once
25 is seen once
30 is seen once
So 15 is the mode.
Therefore, the mean is 21, the median is 20 and the mode is 15.Hope this helps you!
~Just a felicitous girlie
#HaveAMarvellousDay
\(SilentNature :)\)
Mrs. Finch's first grade class was holding a used book sale. Some books were sold for $0.25 anc
others sold for $0.35. The first customer spent $3.15 for 11 books. How many $0.25 books and
$0.35 books did the customer buy?
Answer:
7, 4
Step-by-step explanation:
x = 25 cent books, y = 35 cent books
x + y = 11
.25x + .35y = 3.15 Multiply this to get the x to be the same, x4=
x + 1.4y = 12.6 Now subtract the first equation
-x + y = 11
.4y = 1.6
y = 4
11 - 4 = 7 x = 7
Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 7. What is the approximate probability that will be within 0.5 of the population mean?
Answer:
The probability that the sample mean will be within 0.5 of the population mean is 0.3328.
Step-by-step explanation:
It is provided that a random variable X has mean, μ = 50 and standard deviation, σ = 7.
A random sample of size, n = 36 is selected.
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
\(\mu_{\bar x}=\mu=50\)
And the standard deviation of the distribution of sample mean is given by,
\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{7}{\sqrt{36}}=1.167\)
So, the distribution of the sample mean of X is N (50, 1.167²).
Compute the probability that the sample mean will be within 0.5 of the population mean as follows:
\(P(|\bar X-\mu_{\bar x}|\leq 0.50)=P(-0.50<(\bar X-\mu_{\bar x})<0.50)\)
\(=P(\frac{-0.50}{1167}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.50}{1.167})\\\\=P(-0.43<Z<0.43)\\\\=P(Z<0.43)-P(Z<-0.43)\\\\=0.66640-0.33360\\\\=0.3328\)
Thus, the probability that the sample mean will be within 0.5 of the population mean is 0.3328.
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
Find the limit of the difference quotients for f(x) = x2+2x+1 if a= -1
The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.
To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:
lim(x→-1) [f(x) - f(-1)] / (x - (-1))
First, let's substitute the values into the expression:
lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)
Simplifying further:
lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)
lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)
lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)
Now, we can directly substitute x = -1 into the expression:
\((-1^2 + 2(-1) + 1) / (-1 + 1)\)
(1 - 2 + 1) / (0)
0 / 0
We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.
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Which of these best explains the next step to simplify this expression?
Answer:
Make the -4 exponent in the denominator positive.
17. Consider the function f(x, y, z) = xy ln(yz).
Compute the following partial derivatives:
(a) fx =
(b) fy =
(c) fz =
We can expand
\(f(x,y,z) = xy\ln(yz) = xy \ln(y) + xy\ln(z)\)
Then using the product and chain rules,
\(\dfrac{\partial f}{\partial x} = y\ln(y) + y\ln(z) + \boxed{y\ln(yz)}\)
\(\dfrac{\partial f}{\partial y} = x\ln(y) + \dfrac{xy}y + x\ln(z) = \boxed{x\ln(yz) + x}\)
\(\dfrac{\partial f}{\partial z} = \boxed{\dfrac{xy}z}\)
Please help me please help me help please help me
The width of a rectangle is 4n - 4.5 feet and the length is 4.5n + 9 feet. Find the perimeter of the
rectangle.
9514 1404 393
Answer:
17n+9 feet
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(L +W)
P = 2((4.5n +9) +(4n -4.5)) = 2(8.5n +4.5)
P = 17n +9
The perimeter of the rectangle is 17n +9 feet.
Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene
Answer:
Perimeter = 32.3
Area = 95.24
Step-by-step explanation:
Given:
△ABC, m∠A=60°
m∠C=45°, AB = 9
To find:
Perimeter of △ABC
Area of △ABC
Solution:
Using angle sum property in a triangle:
m∠A + m∠B + m∠C = 180°
m∠B = 180° - 45° - 60° = 75°
As per Sine Rule:
\(\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}\)
Where
\(a\) is the side opposite to \(\angle A\)
\(b\) is the side opposite to \(\angle B\)
\(c\) is the side opposite to \(\angle C\)
\(\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08\)
\(\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22\)
Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3
Area of a triangle is given as:
\(\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)\)
\(\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}\)
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons?
Paying 20 points
A foot contains 12 inches 5 inches is what fraction of a foot
Answer:
5/12 inches
Step-by-step explanation:
also, stop deleting my answers whoever you are
Answer:
5/12
Step-by-step explanation:
5/12 it is very easy
Evaluate the expression: 56/-4
Answer:
\( \frac{ 56}{ - 4} = - 14\)
Hope it helps...........................
An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure. The value of x is degrees, and the value of y is degrees.
Answer:
Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.
1 when this type of variable is passed into a method, any changes made to it in the method are saved and the previous value of the variable is overwritten outside the method.
The type of variable being referred to is a reference variable, also known as a reference type.
In Java and other object-oriented programming languages, reference variables are used to store references to objects. Unlike primitive data types such as int or double, reference variables do not store values directly. Instead, they store the memory address of an object.
When a reference variable is passed into a method, the method receives a reference to the same object as the caller. Any changes made to the object within the method are saved, and the previous value of the object is overwritten outside the method. This is because the method operates on the same object as the caller, rather than a copy of the object.
It is important to understand the behavior of reference variables when passing them into methods, as this can have unintended consequences. For example, if the method modifies the object in a way that is not expected, the caller will also see the same change. To avoid this, it is sometimes necessary to create a new object within the method, rather than modifying the original object.
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10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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Lauren has a garden in the shape of a rectangle where the length is 5.4 meters and 1.5 meters. She plans on increasing both the length and width by 40%
Answer:
5.4 = 7.56
1.5 = 2.1
Step-by-step explanation:
Just find the answer for 40% of the given meters.
determine the measure of each of the following. a. Arc length of AE b. Arc length of DB c. Area of sector DCB d. Area of shaded region of sector BD
Solution:
Given the figure below:
A) Arc length of AE.
Thus, we have the length of the arc AE to be
\(\begin{gathered} length\text{ or arc AE=}\frac{130}{360}\times2\times\pi\times5 \\ =11.34464\text{ inches} \end{gathered}\)B) Arc length of DB
The length of the arc DB is evaluated as
\(\begin{gathered} length\text{ of arc DB=}\frac{130}{360}\times2\times\pi\times7 \\ =15.88249\text{ inches} \end{gathered}\)C) Area of sector DCB
The area of the sector DCB is evaluated as
\(\begin{gathered} area\text{ of sector DFB=}\frac{130}{360}\times\pi\times7\times7 \\ =55.58873\text{ square inches} \end{gathered}\)D) Area of shaded region of sector BD
The area of the shaded region is expressed as
\(area\text{ of big circle - area of small circle}\)Thus, we have the area of the shaded region to be
\(\begin{gathered} area\text{ of shaded region = \lparen}\pi\times7\times7)-(\pi\times5\times5) \\ =49\pi-25\pi \\ =24\pi \\ =75.39822\text{ square inches} \end{gathered}\)
can some please help me with this
Answer:
b) AB congruent to DC
Step-by-step explanation:
SSS Cobgruence Criterion simply says that if all the three corresponding sides of two triangles are same in length..
then the triangles are congruent..
Here, We are already given that AD=ED and BE=EC.. hence, to prove through the SSS criterion we just need to represent that AB=DC
the angel of elevation from a ball on a football field to the top of a 30 foot tall goal post 16 degree 42'. How far is the football from the base of the goal post? Round to the nearest tenth of a foot.
The football is approximately 96.4 feet from the base of the goal post.
What is tangent function?The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:
tan(theta) = opposing / adjacent.
When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.
Given, the angle of elevation is 16 degrees 42'.
That is,
Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees
Using tangent function we have:
tan(16.7) = 30/x
x = 30 / tan(16.7)
x = 96.4 feet
Hence, the football is approximately 96.4 feet from the base of the goal post.
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How do you solve -2 1/2+3/4÷3/8
Step-by-step explanation:
1. use PEMDAS (Parentheses, Exponent, Multiplication & Division, Addition & Subtraction). you would do 3/4 divided by 3/8 first.
3/4 / 3/8 = 2
2. add 2 to -2 1/2 (or if it's easier to understand, do 2 minus 2 1/2)
-2 1/2 + 2 = -1/2 OR 2- 2 1/2 = -1/2
answer is -1/2