Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $984.20. How many pounds of type A coffee were used?

Answer:

35

Step-by-step explanation:

The formula for the variance of a sample is:

Variance = Σ (x - average)^2 / (n - 1)

Where n is the sample size and x is each data point.

We are given the variance as 544 and the standard deviation as 4, and we know that:

Standard deviation = sqrt(Variance)

So,

Variance = Standard deviation^2

Variance = 4^2

Variance = 16

Now we have the variance and can find the sample size:

544 = 16 * (n - 1)

n - 1 = 544 / 16

n - 1 = 34

The sample size is n = 35.

The tape diagram is attached in the solution.

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.

Given is an equation x+4 = 17,

We need to draw a tape diagram for the same,

So, for that, since we have x + 4 which is equal to 17, so, we will draw a box, divide into two parts one will show the x part and ine will show the 4 part, and collectively it will show 17.

The value of the x+4 and 17 is the same, because, according to the diagram, the quantity x+4 collectively showing 17, therefore, they have same values.

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The total tax that the business paid on its purchases only was 769720.25.

In order to pay for general public institutions, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.

We must first figure out the complete cost of the goods in order to determine the total taxable income the corporation paid

The cost of the 16,000 network routers is:

16,000 units x $79.25/unit = $1,268,000

The cost of the 12,000 wireless LAN adapters is:

12,000 units x $129.95/unit = $1,559,400

The cost of the 13,500 computer boards is:

13,500 units x $229.15/unit = $3,092,025

The total cost of all purchases is:

$1,268,000 + $1,559,400 + $3,092,025 = $5,919,425

To calculate the total tax amount, we need to multiply the total cost by the tax rate. Assuming a tax rate of 13%, the total tax amount is:

$5,919,425 x 0.13 = $768,527.25

Therefore, the total tax amount that the company paid on their purchases only is $768,527.25, rounded off to 2 decimal places.

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Answer: 6.3%

Step-by-step explanation:

The probability that the same song is played twice = Number of favourite outcomes / Total outcomes.

= 1 / 6

= 0.0625

in per cent = 6.25%

Probability to the nearest tenth of % = 6.3%

.: Probability - Probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability can be expressed as proportional that ranging from 0 to 1.

They can also be expressed as percentages ranging from 0% to 100%.

The required slope of the line is -1/4 which passes through points (1,-1) and (5,-2).

The slope of the line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

Given,

Let

x₁ = 1 , y₁ = -1

x₂ = 5, y₂ = -2

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula, and we get

m = (-2 - (-1))/(5 - 1)

m = (-2 + 1)/(4)

m = -1/4

Thus, the required slope of the line is -1/4.

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Standard deviation is the square root of the variance. A mean of squared differences the square root of the variance unit-free the covariance.

The standard deviation is a measure of variance from the mean that includes spread, dispersion, and spread. The standard deviation displays a "typical" deviation from the mean. It is a well-liked measure of variability because it retains the original units of measurement from the data set. There is a small variation when data points are near the mean, and a large variation when they are far from the mean. The values' distance from the mean is determined by the standard deviation. The most common method of measuring dispersion is standard deviation, which is based on all values.

Hence, standard deviation is the square root of the variance.

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Answer: Para encontrar el denominador que falta, podemos utilizar una regla de tres simple. En este caso, queremos encontrar el valor de la segunda fracción, por lo que podemos escribir:

2/7 = 10/x

Para despejar x, podemos multiplicar ambos lados de la ecuación por x y luego dividir por 2:

2/7 * x = 10

x = 10 * 7 / 2

x = 35

Por lo tanto, el denominador que falta en la segunda fracción es 35. La fracción completa es:

2/7 = 10/35

Answer:

you are right

Step-by-step explanation:

Answer:

The 9th term is 30

---------------------------------

Use nth term equation:

We have:

And we need to find the 9th term.

Write the given terms as below and solve for d:

Subtract the first equation  from the second:

The first term is:

Find 9th term:

Answer:

The 9th term is 30

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

use the formula y=mx+b

25.95 is the slope because its a constant arte of change and 50 is the y-intercept because you gain $50 in addition to the slope

Answer:

y=25.95x+50

Step-by-step explanation:

25.95 is the dependent variable, so it is the coefficient. The starting amount, or the y-intercept, is 50. This makes the equation y=25.95x+50.

Answer:2 one

Step-by-step explanation:

Step-by-step explanation:

Ted is correct

When you multiply exponents, they actually add.

Note**

[tex]4x = {4x}^{1} [/tex]

Looking at pearl, when she did

[tex] {2x}^{2} \times 4 {x}^{1} [/tex]

It should have equaled

[tex]8 {x}^{3} [/tex]

Pearl's did not, but Ted's did

Answer:

C

Step-by-step explanation:

The shorter the angle, the shorter the side that lies across from it

In angle order it's 33, 71, 76

The lines across in that order are LK, LJ, JK

Therefore, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

Statistics uses variance as a gauge of difference. The following equation of that number is used to determine the average variance in between data and the mean. It includes all data points in with its computations, in contrast to other numeric measures of variability, by comparing the value of each data point to the mean.

Here,

a.

z1 = (23 - 40) / 12 = -1.42

z2 = (40 - 40) / 12 = 0

P(-1.42 < z < 0) = 0.4199

So, approximately 0.4199 or 41.99% of trucks can be expected to travel between 23 and 40 thousand miles in a​ year.

b.

z1 = (30 - 40) / 12 = -0.83

z2 = (60 - 40) / 12 = 1.67

P(z < -0.83) + P(z > 1.67) = 0.2023 + 0.0475 = 0.2498

So, approximately 24.98% of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a​ year.

c.  Thus:

x = 40 + 1.28(12) = 55.36

So, standard deviation problem solution is at least 90% of the​ trucks can be expected to travel 55,36 miles or less per year.

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Answer:

$500.000 × 0.08 = $40,000

$40,000/12 = $3.333.33

Step-by-step explanation:

El interés simple mensual se puede calcular como una fracción del interés anual. Para calcular el interés simple mensual, primero debemos calcular el interés anual y luego dividirlo entre 12 para obtener el interés mensual.

El interés anual se puede calcular multiplicando el capital por la tasa de interés:

$500,000 × 0.08 = $40,000

Luego, para obtener el interés simple mensual, dividimos el interés anual por 12:

$40,000 / 12 = $3,333.33

Por lo tanto, un capital de $500,000 al 8% de interés simple generará $3,333.33 de interés simple mensual.

The required, given expression is completely factored as  (4y -5)(3x - 5).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the expression 12xy - 15x - 20y + 25, we can use the distributive property to factor out a common factor from each of the first two terms and the last two terms:

12xy - 15x - 20y + 25

= (12x)(y) - (15x)(1) - (20)(y) + (5)(5)

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

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

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

So, the expression is completely factored as, (4y -5)(3x - 5).

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The rate for a ratio of the two different quantities would be 13 over 2 puppies per litter. That is option D.

The total number of puppies that Mallory's Border Collie has = 13 puppies.

The number of litters that the puppies are being placed = 2 litters.

Therefore, the rate of puppies per litter is calculated as follows:

13 puppies = 2 litters

X puppies = 1 litter

Make X the subject of formula;

X = 13×1/2

X= 13/2 puppies per litter

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Answer:Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

Step-by-step explanation:3/1 ur welcome

Answer:

  x = 22

  y = 59

Step-by-step explanation:

You want the values of x and y as shown in the figure where angles (2x)° and (y-15)° are vertical angles, and (2x)° and (2x+2)° are complementary.

Two angles are complementary when their sum is 90°.

  (2x)° +(2x+2)° = 90°

  4x = 88 . . . . . . . . . . . divide by °, subtract 2

  x = 22

Vertical angles have the same measure:

  (2x)° = (y -15)°

  2·22 = y -15 . . . . . . divide by °, substitute for x

  59 = y . . . . . . . . .  add 15

The value of x is 22.

The value of y is 59.

Answer:

[tex]\textsf{LCM}=(x+3)^3(x-3)^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6cm}\underline{Difference of Two Squares Formula}\\\\$a^2-b^2=\left(a+b\right)\left(a-b\right)$\\ \end{minipage}}[/tex]

Factor x² - 9 by applying the Difference of Two Squares formula:

[tex]\begin{aligned}\implies x^2-9&=x^2-3^2\\&=(x+3)(x-3)\end{aligned}[/tex]

Rewrite each of the given expressions as an expansion of their factors:

[tex]\bullet \quad (x-3)^2=(x-3)(x-3)[/tex]

[tex]\bullet \quad x^2-9=(x+3)(x-3)[/tex]

[tex]\bullet \quad (x+3)^3=(x+3)(x+3)(x+3)[/tex]

Therefore, we can see that each expression has a factor of (x - 3), (x + 3) or both (x - 3) and (x + 3).

The least common multiple (LCM) of a, b, and c is the smallest multiplier that is divisible by a, b and c.

Therefore, to find the LCM of the given expressions, multiply each factor with the highest power:

Answer:

Magnitude of force is [tex]||v||\approx16.12\text{ lbs}[/tex]

Step-by-step explanation:

[tex]||v||=\sqrt{x^2+y^2}\\||v||=\sqrt{(-8)^2+(14)^2}\\||v||=\sqrt{64+196}\\||v||=\sqrt{260}\\||v||\approx16.12\text{ lbs}[/tex]

Step-by-step explanation:

Find Object Volume Rotation

Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.

The region R is a triangular region defined by the lines y = x, y = x + 1, x = 0, and x = 3. To find the volume of the object obtained by rotating this region about the x-axis, we can use the method of cylindrical shells.

The height of the cylindrical shell is given by the difference between y = x and y = x + 1, or 1 unit. The radius of the cylindrical shell is given by x. Therefore, the volume of the object is given by:

\begin{align*}

V &= \int_{x=0}^{x=3} \pi x^2 \cdot 1, dx \

&= \pi \int_{x=0}^{x=3} x^2, dx \

&= \pi \left[ \frac{x^3}{3} \right]_{x=0}^{x=3} \

&= \pi \left( \frac{27}{3} - \frac{0}{3} \right) \

&= 9\pi

\end{align*}

So the volume of the object is equal to 9π cubic units.

Answer:

12x^2 + 12

Step-by-step explanation:

1. Remove the parentheses:

x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4

2. Cancel out terms:

8x^2 + 16 + 4x^2 - 4

3. Combine like terms:

12x^2 + 12

Answer:

15 and 8

Step-by-step explanation:

Let the legs be a, b

a+b=23

ab=120

Then, 23b-b^2=120. so b^2-23b+120=0. Thus (b-8)(b-15)=0. Thus b=8,15, and if b=8, then the other length a is 15.

The project average is 100% of the student's grade, and if the student has the given averages, their course grade would be 89%.

The project average is the only component of the student's grade that is not weighted. The homework average accounts for 20% of the grade, while the quiz average accounts for 80%. Therefore, the project average is 100% of the student's grade. If the student has the given averages, then their course grade can be calculated by multiplying the homework and quiz averages by their respective percentages and adding the two products. In this case, the student's course grade would be (95 * 0.2) + (80 * 0.8) + 88 = 89%. The student's course grade would then be rounded to the nearest whole number, which is 89%.

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17) The number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas is:

90% probability: 420.5 + (1.645 x 50) = 545.25 miles

30% probability: 420.5 - (1.645 x 50) = 295.75 miles

50% probability: 420.5 miles

18) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car is:

Upper value: 420.5 + (1 x 50) = 470.5 miles

Lower value: 420.5 - (1 x 50) = 370.5 miles

19) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car is:

Upper value: 420.5 + (2 x 50) = 520.5 miles

Lower value: 420.5 - (2 x 50) = 320.5 miles

20) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car is:

Upper value: 420.5 + (3 x 50) = 570.5 miles

Lower value: 420.5 - (3 x 50) = 270.5 miles

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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The correct answer to the statement is A. True. The equation Ax= b is referred to as a vector equation because it consists of scalars multiplied by vectors.

The matrix A multiplies the input vector x, which results in the output vector b.

In other words, each element of the output vector is a scalar multiple of the corresponding element of the input vector.

Thus, the equation represents a vector equation, which describes the relationship between two vectors.

he equation Ax= b is a fundamental concept in linear algebra and is widely used in various mathematical and scientific fields.

It represents the relationship between a linear transformation represented by the matrix A, the input vector x, and the output vector b.

In this equation, the matrix A acts as a set of coefficients that scale the elements of x to produce the elements of b.

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Answer: (x^3 - 3x^2 + 5x - 3)/(x^2 - 2)

Step-by-step explanation:

It says the volume equals the height multiplied by the base area, or base area x height = volume. Because we are given the volume and the base area, we can plug in the values to get (x^2 - 2) x height = (x^3 - 3x^2 + 5x - 3). Finally, we can divide both sides by (x^2 - 2) to get height = (x^3 - 3x^2 + 5x - 3)/(x^2 - 2).

The value of M when r = 12 and the value of r when M = 224 are 504 and 8 respectively.

Direct proportionality is expressed as;

M ∝ r²

Hence; M = kr²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

M = kr²

k = M/r²

Plug in r = 2 and M = 14

k = 14 / (2)²

k = 14/4

k = 7/2

Now, a) the value of M when r = 12 will b;

M = kr²

M = (7/2) × ( 12 )²

M = (7/2) × 144

M = 504

Next, b) the value of r when M = 224

M = kr²

r = √(M/k)

r = √( 224 ÷ 7/2 )

r = 8

Therefore, the values of M and r are 504 and 8 respectively.

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Answer:

9

Step-by-step explanation:

9 makes it so that each set becomes a whole number.