The sum of two numbers is 42. The sum of the smaller and 4 times the larger is 147. Find the
numbers.

The probability that the student chosen at random is male AND got a "C" is 0.0227.

Conditional probability is the probability of an event (A) occurring given that another event (B) has already occurred. It is denoted by P(A | B) and is read as "the probability of A given B".

The formula for conditional probability is:

P(A | B) = P(A and B) / P(B)

Where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

Here we have

The total number of students is 88

Out of these 88 students, 36 are male

Number of males that got grade C =  2

P(male AND C) =  number of males who got C / total number of students

= 2/88 = 0.02272727272  

Rounding this to 4 decimal places, we get:

P(male AND C) = 0.0227

Therefore

The probability that the student chosen at random is male AND got a "C" is 0.0227.

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The equivalent expression to the given one is the second option:

[tex]log_2( y^4*z^4/x^2)[/tex]

Here you need to remember two logarithmic rules, these are:

[tex]log(x^n) = n*log(x)[/tex]

[tex]log(x) + log(y) = log(x*y)[/tex]

And these work for any base of the logarithm.

Here we start with the expression:

[tex]-2log_2(x) + 4log_2(y)+ 4log_2(z)[/tex]

Using the first one:

[tex]-log_2(x^2) + log_2(y^4) + log_2(z^4)[/tex]

Using the second one:

[tex]log_2( y^4*z^4/x^2)[/tex]

That is the equivalent expression, the second option.

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If triangle has a perimeter of 69 cm, and ratio of side length as 6:7:10, then lengths of sides of triangle are 18 cm, 21 cm, and 30 cm.

The side length of the triangle are in the ratio = 6:7:10,

So, We let the lengths of the sides of the triangle be 6x, 7x, and 10x, where x is a constant.

Since the perimeter of the triangle is 69 cm, we have:

6x + 7x + 10x = 69

Simplifying the equation,

We get;

23x = 69

x = 3

So, the measure of sides of triangle are:

6x = 6×(3) = 18 cm

7x = 7×(3) = 21 cm

10x = 10×(3) = 30 cm

Therefore, the lengths of the sides are 18 cm, 21 cm, and 30 cm.

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The given question is incomplete, the complete question is

The lengths of the sides of a triangle are in the extended ratio 6 : 7 : 10. The perimeter of the triangle is 69 cm. What are the lengths of the sides?

The quotient is x² + x + 4, and the remainder is 2.

x³ + 3x² + 6x + 10 = (x² + x + 4)(x + 2) + 2.

We have,

We can use long division to divide x³ + 3x² + 6x + 10 by x + 2:

      x² + x + 4

   ------------------

x + 2 | x³ + 3x² + 6x + 10

        - x³ + 2x²

       --------

         x² + 6x

         - x² - 2x

         ---------

               4x + 10

               - 4x - 8

               ---------

                     2

Therefore,

The quotient is x² + x + 4, and the remainder is 2.

x³ + 3x² + 6x + 10 = (x² + x + 4)(x + 2) + 2.

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Answer:

n > -2

Step-by-step explanation:

[tex]-2n+1 < 5[/tex]

This is a two-step equation, so the first thing you would do is subtract 1 from both sides of the equation.

[tex]-2n+1-1 < 5-1\\-2n < 4[/tex]

Then, divide -2 from both sides of the equation.

[tex]\frac{-2n}{-2} < \frac{4}{-2} \\[/tex]

The less than symbol will become a greater than symbol because you divided by a negative number.

So the solution is:

[tex]n > -2[/tex]

The time your watch will show at 10 a.m. on the following Monday is 10:14 a.m.

If your watch gains 2 minutes in every 24 hours, that means it gains 1 minute every 12 hours.

At 10 a.m. on the following Monday (7 days after 10 a.m. on Monday):

7 days = 168 hours

12 hours = 1 minute

168 hours = ?

= 168/12

= 14 minutes

Your watch would show 10:14 a.m. on the following Monday, as it gains 1 minute every 12 hours and there are 7 days (168 hours) between Monday 10 a.m. and the following Monday 10 a.m.

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Answer:

Mr. Johnson should be paid $285 for a job requiring 60 hours of work.

Step-by-step explanation:

If Mr. Johnson was paid $190 for 40 hours of work, then we can write:

190/40 = x/60

Where x is the amount he should be paid for 60 hours of work.

To solve for x, we can cross-multiply and simplify:

190 * 60 = 40 * x

11,400 = 40x

x = 11,400/40

x = 285

Therefore, Mr. Johnson should be paid $285 for a job requiring 60 hours of work at the same rate.

We need more information about the property and the specific services required to determine the price of Hillary's home.

Answer:

Unfortunately, without additional information, it is impossible to determine the price of Hillary's home. The range of closing costs provided does not provide enough information to calculate the price of the home.

To determine the price of the home, we would need to know either the exact amount of the closing costs or additional information about the home's value, such as its appraised value or sale price.

Therefore, we cannot determine the price of Hillary's home based on the given information.

Step-by-step explanation:

We only know that the estimated closing costs for her home range from $11,600 to $40,600. Closing costs can vary based on a variety of factors, such as the location of the home, the type of mortgage, and the specific fees charged by the lender and other parties involved in the transaction.

To determine the price of Hillary's home, we would need additional information, such as the appraised value of the home, the amount of the down payment, and the specific closing costs that were incurred.

Answer:   k=6

Step-by-step explanation:

4y=24x           Divide both sides by 4

y=6x

y=kx           you can see k=6

but if they want you to actually prove

substitue y=6x into y=kx

you get

6x=kx     divide both sides by x

6=k

Answer:

The inequality is -5 < x < 4.

x² + (y - 3)² = 36; x² + (y + 8)² =36 represent the circles that have a diameter of 12 units and a center that lies on the Y axis.

We know that the abscissa of coordinates of a point on Y axis is 0.

So the equation of a circle center at (0, k) and radius 'r' is given by,

x² + (y - k)² = r²

Here given that the diameter of the circle must be = 12 units

So the radius of the circle = 12/2 = 6 units.

So the equation of the required circle looks like

x² + (y - k)² = 6², where k is an real number.

x² + (y - k)² = 36

So we can see that the equations x² + (y - 3)² = 36; x² + (y + 8)² =36 can be the equation of the required circle.

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Answer: 4547.30 pesos

Step-by-step explanation:

You can set up proportion

[tex]\frac{x}{370}=\frac{12.29}{1}[/tex]         as long as you put pesos on top and dollars on bottom to set up proportion

now solve for x

x=12.29(370)= 4547.30 pesos

or

you can think of it as if you have 1 dollar and that is 12.29 pesos then 370 dollars would be 370x12.29

=4547.30

The graph that does not represent a function is graph b

From the question, we have the following parameters that can be used in our computation:

Graphs A to C

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

using the above as a guide, we have the following:

The graph b would intersect with a line from the x-axis twice

Hence, the graph is b

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Answer:

Plot the points on the graphing calculator, and then generate the best regression model. That model is:

F = 16.65x + 15.7

The closest equation is D.

Answer:

[tex]\left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

Step-by-step explanation:

When multiplying a constant by a matrix, we have to multiply each element by the constant.

[tex]\dfrac{1}{2} \cdot \left[\begin{array}{c c c c}12 & 64 & 78 & 30\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c} \dfrac{12}{2} & \dfrac{64}{2} & \dfrac{78}{2} & \dfrac{30}{2}\end{array}\right][/tex]

[tex]= \left[\begin{array}{c c c c}6 & 32 & 39 & 15\end{array}\right][/tex]

The center of the circle shown is point S

From the question, we have the following parameters that can be used in our computation:

The circle

By definition, the center of a circle is the point that is equidistant to all points on the circumference of the cirlce

In the given circle, the point that satisfies the above definition is the point S

This means that the circle can also be called the circle S

Hence, the center of the circle shown is S

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Check the picture below.

I need to deposit $5,040.06 each month to reach my goal.

How to calculate the monthly deposit needed to reach your retirement goal?

To calculate the monthly deposit needed to reach your retirement goal, we can use the formula for the present value of an annuity, which is [tex]PMT \times [ \frac{(1 - (1 + r)^{-n})}{r} ] = PV[/tex]

where,

PMT is the monthly payment, r is the interest rate per month (11%/12 = 0.92%), n is the number of months (40 years x 12 months/year = 480 months) and PV is the present value of the annuity (which is my retirement goal of $500,000).

Plugging in the numbers,

[tex]PMT \times [ \frac{(1 - (1 + 0.0092)^{-480}) }{0.0092} ] = 500,000[/tex]

Solving for PMT,

PMT = $500,000 / [(1 - (1 + 0.0092)^(-480)) / 0.0092]

PMT = $500,000 / 99.17

PMT = $5,040.06

Therefore, to reach my retirement goal, you need to deposit $5,040.06 each month for the next 40 years.

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You need to deposit $73.06 each month to reach your goal of $500,000 at retirement at 11% interest.

Two different methods of calculating interest are used in finance: simple interest and compound interest.

Only the initial sum of money borrowed or invested, known as the principal, is used to calculate simple interest. The interest gained or charged is the same each period, and the interest rate is applied to the principal amount for a specific amount of time.

Contrarily, compound interest is determined by taking into account both the original principal as well as any prior interest payments. Each period's interest is combined with the principal, and the resulting sum serves as the foundation for calculating interest in the subsequent month.

The future value of the annuity is calculated using the formula:

[tex]FV = P * (((1 + r)^n - 1) / r)[/tex]

Thus, substituting the values we have:

[tex]500,000 = P * (((1 + 0.00917)^{480 }- 1) / 0.00917)[/tex]

Now,

[tex]P = 500,000 / (((1 + 0.00917)^{480} - 1) / 0.00917)[/tex]

P = $73.06

Hence, you need to deposit $73.06 each month to reach your goal of $500,000 at retirement.

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Applying the principle of similar triangles, the value of x is 6 units

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

To find the value of x in this problem, we have to apply similar triangle theorem here.

(8 + x) / 2√21 = 2√21 / x

cross multiply both sides

x(8 + x) = (2√21)(2√21)

8x + x² = 84

Rewrite the equation;

x² + 8x - 84 = 0

solving for x

x = 6, x= -14

Taking the positive value, the value of x = 6

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OD. 16.27

cylinder 4:3 the ratio if their volumes is (4/3)^3, which simplies to 64/27.So the correct answers is D.

Answer:

To find the p-value, we need to first find the corresponding area in the normal distribution table for the test statistic of 1.75.

Since the sample size (n) is greater than 30 and the population standard deviation is unknown, we use the t-distribution to calculate the p-value.

The degrees of freedom (df) for the t-distribution is n - 1 = 20 - 1 = 19.

Using a t-table or calculator, we can find that the area to the right of 1.75 (with df=19) is approximately 0.049.

Since this is a one-tailed test (the alternative hypothesis is that the mean wait time is greater than 2 minutes), the p-value is equal to the area to the right of the test statistic, which is 0.049.

Therefore, the corresponding p-value is 0.049 (rounded to three decimal places).

Step-by-step explanation:

gg

Here is   the missing line of code is    

if item[0]   > item[1]:

   wins += 1

else:

   losses += 1

The comlete code should look like this:


  scores = [[2, 5], [3, 1], [4, 4], [1, 0], [2,  3] ]

wins = 0

losses = 0

for item in scores:

   if item [0] > item[1] :

       wins += 1

   else:

       losses += 1

print("Number of wins:", wins)

print("Number of losses:", losses)

This code examines the scores of the two teams for each game, and if the home team's score ( item  [0]) is higher than the opponent team's score (item[1  ]), it counts as a victory, and the "wins" variable is increased by one.

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The values of b and c such that y = -11x² + bx + c has vertex (0,8) are given as follows:

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The x-coordinate of the vertex is given as follows:

x = -b/2a.

For this problem, we have that a = -11, and we want a x-coordinate of 0 for the vertex, hence the value of b is given as follows:

b/22 = 0

b = 0.

At the x-coordinate of 0, y assumes a numeric value of 8, hence the value of c is given as follows:

-11(0)² + c = 8

c = 8.

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After considering all the given data we conclude that the generated answers to the sub questions are

a) 120 feet

b) 1200 inches

c) 120 inches tall

d) 72

e) 1

f) 1

g) proportional

a. To evaluate the height of the flagpole needed to support a 30 by 42 feet flag, we can apply the ratio of the height of a flagpole to the width of any flag which is 4 to 1.

This projects that the height of the flagpole is be four times the width of the flag. The width of the flag is 30 feet, so the height of the flagpole should be 4 × 30 feet = 120 feet.

b. If the individual have a model of Ft. McHenry that you need to add a flagpole to that will be proportional to the real pole at the fort and the ratio of the model is 1 inch to 10 feet, then you can apply this ratio to determine how tall the individuals model flagpole should be.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10

10 × 120 = 1200

to get 1200 inches. This means that your model flagpole should be 1200 inches tall.

c. It is given that a model flagpole that is 8 inches tall; this is not the correct size. To evaluate how tall it needs to be, we can use the same ratio as in part b.

The real pole at Fort McHenry is 120 feet tall (as determined in part a), so you can multiply this by 10 to get 1200 inches.

This means that your model flagpole should be 1200/10 = 120 inches tall.

d. To evaluate if the model flag and original flag are similar figures, we can compare their corresponding sides.

The original flag has dimensions of 30 by 42 feet, which is equivalent to 360 by 504 inches. The model flag has dimensions of 5 by 6.3 inches. To determine if they are similar figures, we can compare their corresponding sides using ratios.

The ratio of the length of corresponding sides must be equal for two figures to be similar. The length of corresponding sides for these two flags are:

- Original Flag: Length = 360 inches; Width = 504 inches

- Model Flag: Length = 5 inches; Width = 6.3 inches

To compare these lengths, we can divide each length by its corresponding length on the other figure:

- Length Ratio: (360 / 5) = 72

- Width Ratio: (504 / 6.3) = 80

Since these ratios are not equal, these two flags are not similar figures.

To find out what dimensions would make them similar figures, we can use these ratios as scale factors:

Length Scale Factor: (360 / x) = 72

- Width Scale Factor: (504 / y) = 80

Evaluating for x and y gives us:

- x = (360 / 72) = 5

- y = (504 / 80) = 6.3

This means that if we scaled down the original flag by a factor of 72, its dimensions would be equivalent to those of the model flag.

e. To evaluate the ratio of the perimeter of the model flag in comparison to the original flag using the scale factor from part d:

Perimeter Scale Factor: (72 + 80) / 2 = 76

Model Flag Perimeter: (2 * (5 + 6.3)) = 23.6

- Original Flag Perimeter: (2 * (360 + 504)) = 1688

The ratio of these perimeters is:

Perimeter Ratio: (23.6 / (1688 /76)) ≈ 1

This means that the perimeter of the model flag is approximately equal to that of the original flag.

f. To evaluate the ratio of area between these two flags using scale factor from part d:

- Area Scale Factor: (72 × 80) = 5760

- Model Flag Area: (5 × 6.3) ≈ 31.5

- Original Flag Area: (360 × 504) ≈ 181440

The ratio of these areas is:

Area Ratio: (31.5 / (181440 /5760)) ≈ 1

This means that area of model flag is approximately equal to that of original flag.

g. Here relationship between ratios of perimeter and area is that they are both proportional to each other.

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The height of the shooter is 1.4 feet off the ground.

We need to apply trigonometry. Our best choice will be to use the tangent function, which relates the opposite side (height of the shooter) to the adjacent side (distance from the shooter to the car), using the angle of elevation (2 degrees).

Let h = height of the shooter. Then, we can write:

tangent(2°) = h / 40

We can solve for "h" by multiplying both sides by 40 feet:

h = 40 * tangent(2°)

Using a calculator, we find that:

tangent(2°) = 0.0349

So, we have:

h = 40 * 0.0349

h = 1.396 feet

Therefore, the height of the shooter was approximately 1.4 feet (or 16.8 inches) off the ground.

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Answer:

I'm pretty sure the answer is 14 feet. hope this helps!