The frequency diagram shows the heights of students in a class.
a) How many students were over 145 cm?
b) How many students had a height
between 125 cm and 140 cm?
c) How many students were in the class?

Step-by-step explanation :

Sum of first 50 terms for the AP:

[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]

where ,

On substituting the values , we get :

[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]

[tex] \therefore[/tex] Sum of the first 50 terms is 15100

Using Chebyshev's Theorem, it is found that at least 89% of days have a high temperature between 6.6ºF and 51ºF.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

Considering k = 3, the percentage is of at least 89% and the bounds are given as follows:

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Answer: x+y=22; 150x+350y=4800

Step-by-step explanation:

Step-by-step explanation:

You would find a the same way as finding B, just backwards

[tex]( {x}^{2} - 1)( {x}^{2} + 5)[/tex]

Distributing we get

[tex] {x}^{4} + 5 {x}^{2} - {x}^{2} - 5[/tex]

Simplifying it...

[tex] {x}^{4} + 4 {x}^{2} - 5[/tex]

If you are 25yr old and single with no kids/dependents.  The total Federal Income Taxes is $11,218 and FICA paid is $6,478.

First, you need to determine your taxable income.

Gross income: $84,649

Itemized deductions: $10,211

Tax-deferred retirement contributions: $3,288

Taxable income: $71,150

Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.

The first $10,950 is taxed at 10%: $1,095

The next $32,250 is taxed at 12%: $3,870

The next $28,425 is taxed at 22%: $6,253

The remaining $0 is taxed at 24%: $0

Total federal income tax liability: $11,218

b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.

Social Security tax: $5,240.80

Medicare tax: $1,237.20

Total FICA taxes: $6,478

Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.

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The values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find x

tan60° = 20/x

√3 = 20/x

x = 20/√3

=> [tex]x=\frac{20 \sqrt{3}}{3}[/tex]

Now by using the ratio sin60°

sin60° = 20/y

√3/2  = 20/y

y = 40/√3

[tex]y=\frac{40\sqrt{3}}{3}[/tex]

Hence, the values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

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Step-by-step explanation:

22x + 2y = -14

2y = -22x - 14

y = -11x - 7

The two ways of writing the number 6000 will be 10 x 600 and 100 x 60.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Multiplication is the process of determining the product of two or more numbers in mathematics.

Given that Hassan discovers that the result of two multiples of 10 is 6000.

The two ways can be calculated as:-

10 x 600 = 6000

100 x 60 = 6000

Hence, the two ways are 10 x 600 = 6000 and 100 x 60 = 6000.

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Answer:

(B) "1 to 5."

Step-by-step explanation:

The ratio of single to married instructors is 1 to 5. Since 4 instructors are single out of 24 total instructors, the ratio of single instructors to married instructors is 4 to (24 - 4) = 4 to 20. Simplifying the ratio to its simplest form, we get 4:20 = 1:5, which is the answer choice (B) "1 to 5."

Answer:

C. 5x²-7x-8

Step-by-step explanation:

(-3x²-5x +1 ) + (8x²-2x-9)

Grouping like terms:
(- 3x² + 8x²)  + (- 5x - 2x) + (1 - 9)

=> (5x²) + (-7x) + (-8)

=> 5x² - 7x - 8

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

here, we have,

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value and b is the multiplicative factor.

Let y represent the amount of substance remaining after x hours. Hence:

a = 9375, at x = 4, y = 15:

15 = 9375(b)⁴

b = 0.2

y = 9375(0.2)ˣ

For the 7th hour, x = 7:

y = 9375(0.2)⁷

  = 0.12

The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.

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Answer:

76

Step-by-step explanation:

(16x3)+28

Its 16x3 because there's 3 half hours in 1.5hrs  

Answer:

Step-by-step explanation:

The balance of the savings account after 48 months can be calculated using the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the balance after t years

P is the principal (initial amount)

r is the interest rate (as a decimal)

n is the number of times compounded per year

t is the number of years

Step-by-step, the calculation is as follows:

Convert the interest rate from a percentage to a decimal:

r = 7% = 0.07

Determine the number of times compounded per year:

n = 2 (compounded semi-annually)

Determine the number of years:

t = 48 months / 12 months/year = 4 years

Plug the values into the formula:

A = P * (1 + r/n)^(nt)

A = $3500 * (1 + 0.07/2)^(2 * 4)

Calculate the balance using the formula:

A = $3500 * (1.035)^8

A = $3500 * 1.306769

A = $4588.72

So, the balance in the savings account after 48 months is $4588.72.

Answer: 83%

Step-by-step explanation: Take 250 and divide it by 300

Explanation:

Points B and D are midpoints of segments AC and CE respectively. This is because of the tickmarks indicating congruent segment pieces (AB = BC and CD = DE)

Joining the midpoints together forms a midsegment. The midsegment is half as long as the side parallel to it. This means BD is half as long as AE. Flip things around to say that AE is twice as long as BD.

Using their unit rates, the 12-ounce bottle costs lesser per ounce than the 8-ounce bottle of stay clean shampoo.

The unit rate is the cost per unit.

The unit rate is computed as the quotient of the total cost and the number of units.

The cost of a 12-ounce bottle of stay clean shampoo = $8

The unit rate per ounce of the 12-ounce bottle = $0.67 ($8/12)

The cost of an 8-ounce bottle of stay clean shampoo = $6

The unit rate per ounce of the 8-ounce bottle = $0.75 ($6/8)

Thus, comparing the unit rate of the 12-ounce bottle with the 8-ounce bottle, we can conclude that it costs more per ounce to buy the 8-ounce bottle than the 12-ounce bottle.

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Answer:

5%

Step-by-step explanation:

We can use the formula for simple interest to solve for the interest rate:

I = Prt

where:

I is the interest

P is the principal (the amount borrowed)

r is the interest rate

t is the time in years

We know the principal (P) is $8,500, the interest (I) is $1,785, and the time (t) is 42 months, or 42/12 = 3.5 years. So, we can plug in the values and solve for r:

I = Prt

$1,785 = $8,500 * r * 3.5

$1,785 / $8,500 / 3.5 = r

r = 0.05, or 5%

So, the simple interest rate on Tamaya's car loan was 5%.

Answer:425

Step-by-step explanation:

993-43=950

950/2=425

Answer:

$475

Step-by-step explanation:

Let's call the cost of the dryer x. That means the cost of the washer is x + $43. The combined cost of the two is $993, so we can write the equation:

x + (x + $43) = $993

Expanding the right side:

2x + $43 = $993

Subtracting $43 from both sides:

2x = $950

Dividing both sides by 2:

x = $475

So the cost of the dryer is $475.

The angle measure m<T is equivalent to 78 degrees

Similar triangles are triangles that have similar sides and angles.

From the given triangle

<A = <R

<B = <S

<C = <T

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <T = 180

24 + 78 + <T = 180

102 + <T = 180

<T = 180 - 102
<T = 78 degrees

Hence the measure of m<T from the triangle is 78 degrees

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Answer:

Step-by-step explanation:

The formula for calculating the future value of a continuously compounded investment is:

FV = PV * e^(rt)

where PV is the present value, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.

Plugging in the given values, we get:

FV = 5100 * e^(0.08 * 13) = 5100 * e^1.04 = 5100 * 2.856116786 = 14536.86

So, the future value of the investment after 13 years at an 8% interest rate compounded continuously would be approximately $14,536.86. Rounded to 2 decimal places, this is $14,536.86.

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Answer:

4745

Step-by-step explanation:

Answer: 4745

Step-by-step explanation:

3250 = 100%

Percent Increase = +46%

46% of 3250 = 1495

3250 (100%) + 1495 (46%) = 4745

Answer:

12756pi km

Step-by-step explanation:

Circumference = pi * diameter

Diameter = radius * 2

kilometer = meter/1000

6378000*2= 12756000

diamter = 12756000 meters

12756000/1000 = 12756 kilometers

diameter = 12756 kilometers

12756pi km= circumference

The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

How far apart or how far away items or locations are from one another is measured numerically as distance. A physical quantity, it is typically stated in terms of meters, kilometers, miles, or feet. Given that it simply has magnitude and no direction, distance is a scalar quantity.

Usually, a formula is used to determine the distance between two points. One example is the distance formula in Euclidean geometry, which includes computing the square root of the sum of the squares of the coordinate differences between the two points.

Distance can be measured in a variety of contexts, including physics, where it is used to describe an object's displacement through time, and geography, where it is used to define the separation between two points on the surface of the Earth. It is also frequently used in daily life when people go for walks or runs or when they drive from one area to another to calculate the distance they travel.

There are no holes in the first and last 2 inches of the metal strip, leaving 3410 inches (3414 - 2 - 2) as the remaining length.

We can divide the total remaining length by the number of gaps between the holes to determine the distance between the centers of two adjacent holes. The distance between the 12 holes is determined by the fact that there are 11 gaps between them.

distance = (total length - length of 2 end pieces) / (number of gaps)

distance = (3410 in.) / 11

distance ≈ 310.91 in.

Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.

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The measure of angle that is an exterior angle to B is 95°.

The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.

Given that,

The measure of angle 4 is 120°, and the measure of angle 2 is 35°.

Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.

The sum of an interior and exterior angle is 180°,

∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°

and ∠2+ ∠1 +∠3 = 180°

Also, ∠3 = 180 - ∠4

∠3 = 180 - 120 = 60°

Substitute the values,

∠2+ ∠1 +∠3 = 180°

35 + ∠1 + 60 = 180

∠1 = 180 - 95

∠1  = 85°

Now, ∠1 + ∠5 = 180

∠5 = 180 - 85

∠5 = 95°

Hence, the measure of angle that is an exterior angle to B is 95°.

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The correct question is:

Answer: A) 95 Degrees

Step-by-step explanation:

The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.

What is elimination method?

The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.

We are given two equations as

7x + 14y = 28     ....(1)

5x + 10y = 20     ....(2)

Now, on multiplying equation (1) by 10, we get the equation as

70x + 140y = 280     ....(3)

On multiplying equation (2) by 14, we get the equation as

70x + 140y = 280     ....(4)

Since, we are getting the same equations so, the system has infinitely many solutions.

Hence, the value of x is [0,∞] and y is [0,∞].

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The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of the wood necessary to frame the outside of the railing will be given as,

l² = 32² + 36²

l² = 1,024 + 1,296

l² = 2,320

I = 48.167 inches

The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

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By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.

In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:

y = 5x - 7      .......equation 1.

3y - 2x = -12          .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

-3(5x - 7) - 2x = -12

-15x + 21 - 2x = -12

-17x = -12 - 21

17x = -33

x = -33/17 or -1.94

For the value of y, we have:

y = 5(-33/17) - 7

y = -165/17 - 7

y = 2.71

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The Shanika Company's inventory levels changed during 20Y6. The materials inventory increased, the work in process decreased, and the finished goods slightly increased.

Based on the information provided, it appears that the Shanika Company has gone through some changes in its inventory levels during the 20Y6 period.

The company's materials inventory has increased from $274,730 on January 1 to $346,160 on December 31, indicating that the company has acquired more raw materials over the course of the year.

On the other hand, the work-in-process inventory has decreased from $494,510 to $470,780, suggesting that the company has been able to efficiently process its raw materials into partially completed goods over the year.

Finally, the finished goods inventory has increased slightly from $475,280 to $481,160, indicating that the company has been able to produce more finished products over the course of the year and has had sufficient demand for its products to keep the finished goods inventory at a relatively stable level.

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