Gonzalez Manufacturing borrowed $24000. Part of the money was borrowed at 8%, part at 10%, and part at 12%. The
total amount borrowed at 8% and 10% was twice the amount borrowed at 12%. Find the amount borrowed at each rate if
the annual interest was $2480.
How much money was borrowed at 8%?

Answer:

Step-by-step explanation:

Answer: 2

Answer:2

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

If the age is expressed as a ratio, such as p:q, then qx and px are taken into account as the age. If you assume that you are x years old now, then n times that number is (xn) years. If you're assuming that x is the current age, then 1/n of that number will equal (x/n) years.

calculation

Let's say there is an age difference of x and y,

in which case the answer to question 28 should be 2.03 years:

(x-y)*60/100.

A gap of 2.03 years has a value such that 60% of age disparities are smaller than it.

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The algebraic expression for "The room capacity does not exceed 250" is D. c≤250

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

It should be noted that "the room capacity does not exceed 250" simply means it should be less than or equal to 250. This will be c≤250.

In conclusion, the correct option is D.

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Answer:

Step-by-step explanation:

You want to know the measure of angle 1 given that angle 2 is four times angle 1, and their sum is 95°.

The angle sum theorem tells you the whole is equal to the sum of the parts.

  ∠1 +∠2 = ∠WXZ

Using the given information, we can write ...

  ∠1 + (4×∠1) = 95°

  5×∠1 = 95° . . . . . . . . collect terms

  ∠1 = 19° . . . . . . . . . divide by 5

Then angle 2 is ...

  ∠2 = 4×∠1 = 4×19°

  ∠2 = 76°

6/7

Step-by-step explanation:

1 - x = 1/7

- x = 1/7 - 1

- x = 1/7 - 7/7

- x = -6/7

x = -(-6/7)

x = 6/7

thus,

1 - 6/7 = 1/7

The true statements about the image of the parallelogram are,

The corresponding sides have different lengths.

The parallelograms are congruent.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A parallelogram in a coordinate plane is translated, rotated, and then reflected.

In the case of translation, rotation and reflection would only change its coordinate points, and the preimage and image will be congruent.

The coordinate points of the vertices would only change if given.

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In 3 hour  Mr. Reed can presents 15 presentations.  The division equation and a multiplication equation are 3 ÷ 1/5 =15 and 3 × 5 = 15 respectively.

What is an equation of division?

Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety. The division operator and the numbers that are being divided will both be on one side. The other side displays the result of the division.

The 3 large rectangles represent the 3 hours.

Each presentation is 1/5 hour so each rectangle is divided into 5 equal sections.

From the model you can write the division equation: 3 ÷ 1/5 =15

You can also write the multiplication equation: 3 × 5 = 15

Both equations show 15 projects are presented in 2 hours.

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The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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Answer:

8 17/50

Step-by-step explanation:

8.34

= 8 34/100

8 17/50

Answer: 8_17/50

Step-by-step explanation:

Answer:

None of these

Step-by-step explanation:

[tex]\frac{1}{4}+\frac{1}{2} \cdot \frac{4}{7}=\frac{1}{4}+\frac{4}{14}=\frac{1}{4}+\frac{2}{7}=\frac{7+8}{28}=\frac{15}{28}[/tex]

Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right.

How to carry out Congruence Proofs?

We are told that both peter and Vivian were trying to prove from the attached diagram the statement that;

If ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3.

Now, from the proofs of both of them, we can see that peter used a direct proof because he knew he could get it directly but Vivian utilized another means which was by starting with contradiction to reprove that the answer was correct.

Thus, we can conclude that Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right

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Answer: A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. In the case of the given confidence interval (0.008, 0.094), the interval is estimated to contain the true value of the population parameter with a confidence level of 95%.

To express this confidence interval in the form of p^ - E < p < p^ + E, where p^ is the point estimate of the population parameter and E is the margin of error, we first need to find the point estimate of the population parameter. The point estimate is the midpoint of the confidence interval, which is found by taking the average of the lower and upper bounds of the interval. In the case of the given confidence interval, the point estimate is (0.008 + 0.094) / 2 = 0.051.

The margin of error, E, is found by subtracting the point estimate from the upper and lower bounds of the confidence interval. In the case of the given confidence interval, the margin of error is 0.094 - 0.051 = 0.043 for the upper bound, and 0.051 - 0.008 = 0.043 for the lower bound.

Thus, the given confidence interval can be expressed in the form of p^ - E < p < p^ + E as 0.051 - 0.043 < p < 0.051 + 0.043, which simplifies to 0.008 < p < 0.094. This is the same as the original form of the confidence interval.

Answer:

Mabel will use scale factor of 20 to enlarge the design.

{ If you do need explanation, Please inform me.}

According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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The maximum width Casket that will fit in a standard vault is 28 inches.

Standard measurements may vary significantly depending on the manufacturer.

Caskets normally measure 84 inches long, 28 inches broad, and 23 inches tall. Both wood and metal caskets often have the same proportions. Caskets are intended to fit into normal burial sites, which are generally 30-inches wide and may accommodate ordinary caskets as well as enlarged caskets of 28-inch and 29-inch dimensions.

Casket inside dimensions vary significantly; the metal caskets are typically 78 or 79 inches long and 23 or 24 inches broad.

A typical size casket/coffin is enough for the most majority of individuals. Standard caskets can typically (but not always) fit people up to 6'5" and 350 pounds, but we strongly advise you to speak with your funeral director to determine the precise casket size you require.

The maximum width Casket that will fit in a standard vault is 28 inches.

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First, state the null and alternate hypothesis for the hypothesis test

H0:p=0.52

Ha:p≠0.52

z=pˆ−p/√p(1−p)/n

z= pˆ−p divided by the square root of p(1−p) divided by the sample (n)

z= 0.49^-0.52/ √0.52 ( 1- 0.52) / 340 = -2.24

z=-2.24

When using rejection regions, we reject the null hypothesis, H0, if:

z<−zα for a left-tailed test

z>zα for a right-tailed test

|z|>zα/2 for a two-tailed test

Thus the decision rule is: Reject the null hypothesis, H0, if |z|>2.33.

Since the absolute value of the z test statistic, 2.24, is less than the critical value, 2.33, we fail to reject the null hypothesis.

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Answer:

4th one

Step-by-step explanation:

Hope that helps.

Answer:

y = 120t + 480

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

Answer: D. y=x+4

Step-by-step explanation:

1. The equation will have the same slope

2. Plug in the given point to find b, the y-intercept

Answer: 10.5 pounds of clay

Step-by-step explanation:

We know she uses three and one-half pounds of clay to make seven small vases.

3 1/2 = 3.5

21 is 3 times 7

So We take 3.5 times 3 = 10.5 pounds of clay

she will use 10.5 pounds of clay to make 21 small vases.

question, we have to calculate the ratio by dividing a by b we will get the ratio as [tex]\frac{4}{3}[/tex].

Using the ratio formula, ratios can be represented as a fraction. The ratio formula for any two quantities says a and b, is a:b = a/b. Because a and b are individual amounts for two portions, the total quantity is given as (a + b).

Known Total Amount

Determine the total quantity to be produced.

Determine the total number of parts in the ratio.

Divide the total quantity made by the total number of parts to get the amount per part.

Calculate the amount of each ingredient by multiplying each component by the amount per part.

Given:

Here is the ratio of eggs to flour

Eggs(a)     0    2     4    6

Flour(b)     0   1.5   3    4.5

For the table look at the image.

as per the question, we have to calculate the ratio by dividing a by b we will get the ratios as [tex]\frac{4}{3}[/tex].

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Answer:

Option 3:  the function that goes through the point (3, 5) is f(x-5)-1

Step-by-step explanation:

To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).

For option 1, f(x-5)+1, we have:

f(3-5)+1 = f(-2)+1 = 6+1 = 7

For option 2, f(x+5)-1, we have:

f(3+5)-1 = f(8)-1 = ?

For option 3, f(x-5)-1, we have:

f(3-5)-1 = f(-2)-1 = 6-1 = 5

For option 4, f(x+5)+1, we have:

f(3+5)+1 = f(8)+1 = ?

Answer:

Elimination is the adding or subtracting of two equations used to solve them.

Step-by-step explanation:

Elimination is the adding or subtracting of two equations used to solve them.

Say you have this equation. [tex]\left \{ {{x + y=2} \atop {-x+y=6}} \right.[/tex]

Notice that the x in both equations are opposites. After adding together we get.

x + y - x + y = 2 + 6

2y = 8

y = 4

x + 4 = 2

x = - 2

(- 2,4)

Say you decide to subtract the equations.

[tex]\left \{ {{x+y=2} \atop {x+2y=8}} \right.[/tex]

x + y - x - 2y = 2 - 8

- y = - 6

y = 6

x + 6 = 2

x = - 4

(- 4, 6)

You can also multiply equations to make it easier to substitute.

[tex]\left \{ {{y+x=4} \atop {-2y+2x=8}} \right.[/tex]

[tex]\left \{ {{2y+2x=8} \atop {-2y+2x=8}} \right.[/tex]

2y + 2x - 2y + 2x = 8 + 8

4x = 16

x = 4

y + 4 = 4

y = 0

(4, 0)

Answer:

[tex]\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}[/tex]

Step-by-step explanation:

[tex]\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}[/tex]

The length of A in the triangle is obtained as follows:

a = 282.74 cm.

The first step in obtaining the missing side length is obtaining the measure of the missing angle.

The sum of the measures of the internal angles of a triangle is of 180º.

The angle measures for this triangle are given as follows:

Then we have that:

Then the length of a is obtained applying the law of sines as follows:

sin(26º)/a = sin(106º)/620

Applying cross multiplication, we have that:

a = 620 x sin(26º)/sin(106º)

a = 282.74 cm.

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Answer:

the real answer is 1051

Step-by-step explanation:

The volume of the rectangular block in this problem is given as follows:

1300 cm³.

The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:

V = length x width x height.

The dimensions for this block are given as follows:

However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:

Hence the volume of the rectangular block can be calculated as follows:

V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.

(total volume subtracted by the removed volume from the empty space at the middle).

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