Work out the length of DB in the diagram below.
Not drawn
to scale
С
5 cm
D
B
4 cm
E
А
18 cm

Answer:

6x+2

Step-by-step explanation:

Answer:

\( x = \sqrt {40}\)

Step-by-step explanation:

Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:

\( {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ \)

Answer:

D. x = sqrt(52).

Step-by-step explanation:

Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.

a^2 + b^2 = x^2

4^2 + 6^2 = x^2

16 + 36 = x^2

52 = x^2

x = sqrt(52)

x = sqrt(2 * 2 * 13)

x = 2sqrt(13)

x = 7.211102551.

Hope this helps!

Probability that an ace is pulled from the deck = A/T=4/52=1/13

52 cards are there in all.

Four aces are found in all of the card A's.

Thirteen spades in all.

Probability that an ace is pulled from the deck = A/T=4/52=1/13

likelihood that a spade will be the next card drawn =S/T=13/52=1/4

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The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

3/4 x 1/4 = 3/16 in fraction form. 3/4 x 1/4 = 0.1875 in decimal form.

Answer:

3/16  your welcome hehe

Step-by-step explanation:

a. The hole in the ball is 12 cm deep

b. The radius will be 25 cm

From the question, we are to determine how deep the hole in the spherical steel ball is

To calculate how deep the hole is, we will determine the height of the cylinder

From the given diagram, using the Pythagorean theorem,

We can write that

13² = x² + 5²

Solve for x

13² = x² + 5²

169 = x² + 25

Subtract 25 from both sides of the equation

169 - 25 = x² + 25 - 25

144 = x²

Therefore

x² = 144

x = √144

x = 12 cm

The hole is 12 cm deep

b. To calculate the radius of the ball with a similar hole 7 cm and 24 cm deep

We will also used the Pythagorean theorem,

Let the radius by y, then we can write that

y² = 7² + 24²

x² = 49 + 576

x² = 625

x = √625

x = 25 cm

Hence, the radius will be 25 cm

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Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

y = -7x -4

Step-by-step explanation:

Slope-intercept form: y = mx + b

given:

m = -7

b = -4

answer: y = -7x -4

hope this helps :)

Answer:

(0,-5)

Step-by-step explanation:

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

x < -50

Step-by-step explanation:

\(5-\frac{1}{2}x>30\)

\(<=>-\frac{1}{2}x >30-5\)

\(<=> x<25:-\frac{1}{2}\)

\(<=>x<-50\)

Answer:

Option 2

Step-by-step explanation:

Thus, , the physical therapist should form a sample size of 601 to determine the difference in the proportion of men and women.

To determine the sample size needed for a physical therapist to estimate the difference in the proportion of men and women participating in regular sustained physical activity within four percentage points and with 95% confidence, we can use the formula for sample size estimation in proportion-based studies.

The formula is: n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score for the desired confidence level (1.96 for 95% confidence)
- p is the estimated proportion (use 0.5 if no prior information is available)
- E is the margin of error (0.04 for four percentage points)

Plugging in the values, we get:

n = (1.96^2 * 0.5 * 0.5) / 0.04^2
n ≈ 600.25

Since the sample size must be a whole number, we round up to the nearest whole number, which is 601.

Therefore, the physical therapist should obtain a sample size of 601 to estimate the difference in the proportion of men and women participating in regular sustained physical activity within four percentage points and with 95% confidence.

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Answer:

He Melanie ,  use SOH  CAH  TOA to remember the trig functions

Step-by-step explanation:

for 14 they hyp = 22 and we know one angle of 45°,  we also know that the triangle has a right angle or 90°  and by inspection we can tell that the other angle is also going to be 45°   so we know X and Y will be the same length, is why this is a good observation.  

Use one of the trig functions with H in it b/c you know Hyp is 22,  so,  

SOH  =  Sin(Θ)= Opp / Hyp  

Sin(45) = Opp / 22

Sin(45) * 22 = Opp

\(\sqrt{2}\) / 2  * 22 = opp

11*\(\sqrt{2}\) = opp     is the exact answer,   if  you would like some decimal places, it's 7.7781 units,  both X and Y

for 15  we can use SOH again for the bigger triangle.  we know the Hyp is 24 and the angle is 30°

Sin(30) = Opp / 24

Sin(30) *24 = Opp

12 = Opp         ( Because I know Sin(30)  = 1/2 )

Opp is the upright between the two triangles

Use CAH   Cos(Θ) = Adj / Hyp

Cos(30) = Adj / 24

Cos(30) * 24 = Adj

\(\sqrt{3}\) /2 *24 =Adj

12\(\sqrt{3}\) = Adj

Z = 12\(\sqrt{3}\)   or if you want some decimals 20.7846

Becasue the smaller triangle is also a 45° right triangle we know that the upright and side Y are the same lengths

then

Y = 12

You could use SOH or CAH  to find the Hyp but, lets just resort to Pythagoras,  and use  his formula to find Hyp

Hyp = \(\sqrt{12^{2} +12^{2} }\)

Hyp = \(\sqrt{288}\)

hyp = 16.97

X = 16.97

:)

To start seeing a profit after selling 230 units, the major appliance store needs to consider both the cost of purchasing the vacuums and the delivery fee. The total cost of purchasing 230 vacuums would be: $86 x 230 = $19,780 Adding the delivery fee of $9,200, the total cost becomes:$19,780 + $9,200 = $28,980

To determine how much the store should charge for the vacuums, let's first calculate the total cost of purchasing and delivering 230 units.

1. Find the cost of purchasing 230 vacuums at $86 each:
230 vacuums * $86/vacuum = $19,780

2. Add the delivery fee of $9,200 to the cost of purchasing the vacuums:
$19,780 + $9,200 = $28,980

3. Since the store needs to start seeing a profit after 230 units are sold, we can calculate the minimum price per vacuum they need to charge:
Total cost / 230 units = Minimum price per vacuum
$28,980 / 230 units = $126

So, the store should charge at least $126 for each vacuum to start seeing a profit after selling 230 units.

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The Steady-state gain can be found using the formula Kp = lim s->0 G(s).

A. (a) The inverse Laplace transform of the function 8 /s² (s+2) is given by f(t) = 8(t - e^(-2t)).

B. (a) To find the inverse Laplace transform of 8 /s² (s+2), we can use partial fraction decomposition and inverse Laplace transform tables.

First, we express the function in partial fraction form as follows: 8 /s² (s+2) = A/s + B/s² + C/(s+2).

To find the values of A, B, and C, we can equate the coefficients of corresponding powers of s in the numerator and denominator. This leads to the equations A + 2B + 2C = 0, A = 8, and B = -8.

Substituting the values of A and B into the equation A + 2B + 2C = 0, we find C = 4.

Now, we have the partial fraction decomposition as: 8 /s² (s+2) = 8/s - 8/s² + 4/(s+2).

Using inverse Laplace transform tables, we find the inverse Laplace transforms of each term: L⁻¹{8/s} = 8, L⁻¹{8/s²} = 8t, and L⁻¹{4/(s+2)} = 4e^(-2t).

Finally, we combine the inverse Laplace transforms of each term to obtain the inverse Laplace transform of the original function: f(t) = 8(t - e^(-2t)).

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Answer:

n=16

Step-by-step explanation:

3 (n-4) = 36

3n -12=36

add twelve to both sides. because -12 + 12 is 0. and once you are at zero, you can cancel it out.

3n=48

divide by 3 on both sides

n=16

Im not 100% sure what youre asking but if the value for C isnt given then it would be -7c because 3-10 is -7

(if theres a value for C can you let me know I can solve the actual thing it it would help more just lmk :)

Answer:

-7c

Step-by-step explanation:

your welcomeeeeeeeeee

The probability of selecting at least one defective item at random is 0.3017.

The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.

Defect rate = P(defect) = 0.05

Probability is defined as the required outcome divided by the total number of possible outcomes.

P( at least 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95

P(none is defective) = P(non defective)^7

P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983

P(at least one is defective) = 1 - 0.6983 = 0.3017

Therefore, probability of at least one defective item is 0.3017.

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The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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The value of (double)(5/2) is 2.0. In the expression (double)(5/2), the division operation 5/2 is performed using integer division because both 5 and 2 are integers.

Integer division truncates the decimal part of the result and returns the quotient as an integer. In this case, 5 divided by 2 is equal to 2.

However, by explicitly casting the result to a double (using the (double) operator), we convert the integer value 2 to a double value, which becomes 2.0.

Therefore, the value of (double)(5/2) is 2.0, as the division is performed as an integer division followed by a casting to a double.

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A ratio variable should be transformed into a dichotomous variable represented with dummy coding when the research question or analysis requires a simplified comparison between two distinct groups, the relationship between the ratio variable and the outcome variable is non-linear, there is a meaningful cutoff or threshold value, or specific statistical methods necessitate dichotomous variables.

A ratio variable may be transformed into a dichotomous variable represented with dummy coding under the following conditions:

Simplification of Analysis: When the research question or analysis requires a simplified comparison between two distinct groups or categories based on the ratio variable.

Nonlinearity: If the relationship between the ratio variable and the outcome variable is non-linear, it may be beneficial to dichotomize the ratio variable to capture the presence or absence of a certain condition or threshold.

Practical Interpretation: When there is a meaningful and interpretable cutoff or threshold value for the ratio variable that divides the population into two distinct groups.

Statistical Analysis Requirements: Certain statistical methods or models may require dichotomous variables for analysis, and transforming a ratio variable into a dichotomous variable allows for the use of these methods.

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Answer:

200.5ft²

Step-by-step explanation:

According to my calculation this is the answer ..

Answer:

8

the answer is 806

Step-by-step explanation:

840-36=806

Answer:

80n + 20

Step-by-step explanation:

20 stays the same because it's a one time fee. Then, for every night the Harvey family stays, it costs them eighty dollars. So, it's 80n + 20

Answer: 80n+20

Step-by-step explanation:

80 is the cost of nights you stayed but you don’t know the number of nights they dated so you place n next to 80 and they payed an additional 20 fee so you add that to 80n

Answer:

x ≤ 13

Step-by-step explanation:

hope this helps

Answer:

x/7 + 9 = 6

Step-by-step explanation:

Hope this helps! Please give brainliest!

Answer:

Step-by-step explanation:

a hexagonal prism is made up of two bases that are hexagons and six faces that are rectangles.

Lateral surface area, LA = Perimeter × height

Perimeter = number of sides × length of each side

Perimeter, P = 6 × 10 = 60

LA = 60 × 12 = 720 units squared

Area of each base, B = 1/2a × perimeter

Where

a = apotherm

We would determine the length of the apotherm of each base of the prism by applying the formula,

a = s/[2tan(180/n)]

Where

s = length of each side = 10

n = 6 sides

a = 10/[2tan(180/6) = 10/[2tan30)

a = 8.66

B = 1/2 × 8.66 × 60 = 259.8

Total surface area = LA + 2B

Total surface area = 720 + 2 × 259.8 = 1239.6 units squared

The relationship between the angles depend on their relative positions.

Response:

The possible drawing in the question created based on the relationship between the angles is attached.

∠a and ∠c;

∠a and ∠b

∠b and ∠h

∠f and 55°

∠a and ∠e

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The correct statements about the synthetic division are C, D, F.

It should be noted that 4x² - 17x - 15 will be:

= 4x² - 20x - 3x - 15

= (x - 5)(4x + 3)

The roots of the polynomial will be:

= f(x) = 0

(x - 5) = 0

x = 5

4x + 3 = 0

x = -3/4

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