\( \sf\sqrt{256} \)
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Answer:

If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

9514 1404 393

Answer:

  False

Step-by-step explanation:

f(-2) = (1/2)(-2) -3 = -1 -3 = -4

g(-2) = -2(-2) +2 = 4 +2 = 6

The function values are not the same at x=-2, so the graphs do not intersect there.

__

The graphs intersect at x=2.

The probability that someone is in the right job and the test is then wrong is 0.195.

The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is:

= 0.65*0.3

= 0.195

The probability that someone is in the wrong job and the test is right is:

= 0.35 × 0.3

= 0.105.

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The required number of cup of milk required to make 87 cookies.

While you're discussing a recipe, you can make sense of what fixings are required by talking about that the recipe "calls for ___". For instance: It calls for olive oil.

A recipe calls for of a cup of milk for 29 cookies.

It means we need 29 cookies for one cup of milk,

To find number of cup need to make 87 cookies.

Then,

29 cookies = one cup

one cookie = one cup/29

87 cookies = 87/29 cup of milk

3 cup of milk

Thus, there are 3 cup of milk required.

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Answer:

f(x)=11

g(x)=8

Step-by-step explanation:

f(x)=(2)+9=11

g(x)=4(2)=8

BRAINLIEST PLEASE

Answer:

x = 3  rounded to the nearest whole number (actually 2.735)

Step-by-step explanation:

The triangle formed by the sides of length 7x, 12x and 32 form a right triangle with the side of length 32 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

38² = (7x)² + (12x)²

1,444 = 49x² + 144x² = 193x²

Switching sides:

193x² = 1444

x² = 1444/193 = 7.48

x = √7.48= 2.735 = 3  rounded to the nearest whole number

Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

Answer:

1/2

Step-by-step explanation:

Divide both parts by 7

1/2

Hope this helps :)

Answer:

a) Not confident in the outcome.

b) Confident A would win.

c)Confident A would win.

d) Not confident in the outcome.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

These bounds are related to the previous estimate and to the margin of error.

The lower bound is the estimate subtracted by the margin of error.

The upper bound is the margin of error added to the estimate.

Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll.

Here, we need the lower bound of the confidence interval for the percentage of votes of the candidate A above 50%.

a. Candidate A: 54% Candidate B: 46% Margin of error: ± 5% Confident A would win or Not confident in the outcome

54 - 5 = 49%

Not confident in the outcome.

b. Candidate A: 52% Candidate B: 48% Margin of error: ± 1% Confident A would win or Not confident in the outcome

52 - 1 = 51%

Confident A would win.

c. Candidate A: 53% Candidate B: 47% Margin of error: ± 2% Confident A would win or Not confident in the outcome

53 - 2 = 51%

Confident A would win.

d. Candidate A: 58% Candidate B: 42% Margin of error: ± 10% Confident A would win or Not confident in the outcome

58 - 10 = 48%

Not confident in the outcome.

By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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Answer:

Second test

Step-by-step explanation:

Given that :

FIRST TEST

Mean (m) = 325

Standard deviation (s) = 100

Score (x) = 425

SECOND TEST

Mean (m) = 50

Standard deviation (s) = 6

Score (x) = 65

Express both scores as standardized scores:

Zscore = (x - m) / s

First Score :

Zscore = (425 - 325) / 100

Zscore = 100/100 = 1

SECOND SCORE :

Zscore = (65 - 50) / 6

Zscore = 15 / 6 = 2.5

Student performed better on second test :

Zscore second > Zscore first

Answer:

Area = 200 + 50 + x

Step-by-step explanation:

Given

Length = 20

Width = 30

Side Walk = x

Required

Determine the area.

To do this we need to get the new worth and length by adding the length of the sidewalk.

This gives:

Length = 20 + x.

Width = 30 + x

So, area becomes.

Area = (20 + x)(30 + x)

Area = 600 + 20x + 30x + x²

Area = 200 + 50 + x²

Answer:

The answer is -40

Step-by-step explanation:

Answer:  19x - 216/6

Explanation: Hope this helps!

Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Answer:

\(112in^{2}\)

Step-by-step explanation:

to find the area of the square we multiply the base x height so 10x10 which equals 100in^2.

to find the area of the triangle we multiply the base x  height divided by 2 so to find the base 10-6 will give us the dotted line which equals 4. to find the height of the triangle we take 16-10 which equals 6. to find the area of the triangle we multiply 6x4/2 to make 12 in^2. to find the total area we add the triangle plus the square 100+12=112in^2

Answer: 7/2

Step-by-step explanation: To make an improper fraction we need to multiply the whole number by the denominator and then add the numerator. Than we take that new number as the numerator and keep the original denominator the same. 3 multiplied by 2 is 6. 6 plus 1 is 7. We keep the 2 as the denominator and or improper fraction is 7/2.

-Hope this helps:)

Point D is the midpoint of segment GH.

A point on a line that divides the line into the equal line segments is called midpoint.

In the given diagram,

given lines are GH and CF.

Also given that,

GD = DH

Since, D bisects line GH into two equal parts, therefore by using midpoint property,

D is the midpoint of segment GH.

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Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.

Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.

In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.

For example, two people could own different numbers of credit cards but have the same monthly charges.

As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).

Because of this, case 3 does not represent a function.

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The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

The percentage of confidence intervals that would capture the true population means is approximately 95% of them. which is the correct answer would be option (C).

There were 100 random samples of the same size drawn from a population known to have a normal distribution with a mean and a standard deviation.

For each of the 100 random samples, a 95% confidence interval for the population mean was created.

Since all the conditions are satisfied,

Therefore, the percentage of confidence intervals that would capture the true population means is approximately 95% of them.

Hence, the correct answer would be an option (C).

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Step-by-step explanation:

h more than 172 is the same as 32

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

D) 2

Step-by-step explanation:

1/15×120/4

1/15×30

1×2

2

Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer