Solve |2x - 2| < 8

{x|-3 < x < 5}
{x|x < -3 or x > 5}
{x|-5 < x < 3}

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Slope means inclination of the line, with respect to horizontal line x.

y-intercept is the point where line touches y line axis

Now draw line with given slope and intercept

y= mx + b

y= -6x -2

then m= -6 , and b= -2

m = -6 means go 1 unit to right, and 6 units up

Answer:

2.55

Step-by-step explanation:

3/4 is equivalent to 0.75

So,

12 3/4 is equivalent to 12.75

so,

12.75 acres/5 children= 2.55 acres per child

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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The value of x in the statement negative 3 less than 4.9 times a number x is the same as 12.8 is 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given a statement negative 3 less than 4.9 times a number, x, is the same as 12.8 this can be numerically expressed as,

4.9x - (- 3) = 12.8.

4.9x + 3 = 12.8

4.9x = 12.8 - 3.

4.9x = 9.8.

x = 9.8/4.9.

x = 2.

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The expression for sentence "a third of a number n" is n/3.

When we say "a third of a number n," we mean dividing the number "n" by 3.

Mathematically, we represent it as:

a third of n = n/3

If we have a certain number "n," taking one-third of that number is the same as dividing "n" by 3.

This operation yields a value that is one-third of the original number "n."

Hence, a third of a number n is n/3.

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The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

30% of 30 has the least value out of all answer choices.

Step-by-step explanation:

Solve for the values of the given percentages of each number:

30% of 50:

Divide 50 by 100 to get 1%

50/100 = 0.5

Multiply 1% (0.5) by 50:

0.5 x 50 = 15

So 30% of 50 = 15

50 % of 30:

50% of a number means half of it since 50% is half of 100% so:

30/2 = 15

So 50% of 30 = 15

30% of 30:

Divide 30 by 100 to get 1%:

30/100 = 0.3

Multiply 1% (0.3) by 30:

0.3 x 30 = 9

So 30% of 30 = 9

50% of 50

50% of a number means half of it since 50% is half of 100% so:

50/2 = 25

So 50% of 50 = 25

Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:

25, 15, 15, 9

9 is the most least, it is the value equal to the answer choice “30% of 30”

HOPE THIS HELPED!

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Answer:

5

Step-by-step explanation:

the in put would need to be 5 cuz :

-2 x 5 + 5

-10 + 5

-5

Answer:5

Step-by-step explanation:

Answer:

????? what?

Step-by-step explanation:

Answer:

i dont speak spanish

Step-by-step explanation:

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)

Answer:

Step-by-step explanation:

Rounded to the underlined digit, 84.59 becomes 84.6.

Rounding a number means approximating it to a specified place value. In this case, we are rounding 84.59 to the nearest tenth, which is the first digit to the right of the decimal point.

1. Identify the Digit:

Underline the digit in the tenth's place, which is 5 in 84.59.

2. Look at the Next Digit:

The digit immediately to the right of 5 is 9. Since 9 is greater than or equal to 5, we round up the underlined digit.

3. Adjust the Digit: Add 1 to the underlined digit, which becomes

6 (5 + 1 = 6).

4. Replace Other Digits: Keep all the digits to the left of the underlined digit unchanged. Therefore, the 84 remains the same.

5. Final Result: The rounded number is 84.6.

So, when rounding 84.59 to the nearest tenth, we get 84.6. Rounding helps make numbers easier to work with when precision beyond a certain point is not necessary.

Remember that when the digit to the right of the one you're rounding to is 5 or greater, you round up, and when it's less than 5, you round down.

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Answer:

i think is 3.3 but i dont know

Step-by-step explanation:

Answer:

$20.52

Step-by-step explanation:

19x0.08 (that's 8% or 8/100) = $1.52

$19+$1.52= $20.52 :)

Answer:

\(\dfrac{x\sqrt{4-x^2}}{4-x^2}\)

Step-by-step explanation:

Given:

\(\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)\)

\(\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}\)

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}\)

Simplify the denominator:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}\)

\(\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}\)

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}\)

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}\)

Simplify:

\(\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}\)

Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

Answer:

C

Step-by-step explanation:

60÷6=10, 90÷9=9, 75÷7.5=10, It divided by 10 so it's 1/10

The scale factor of dilation of the triangle is k = 1/10

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the first triangle be ΔXYZ

Let the second triangle be ΔUVW

Now , the measure of sides of ΔXYZ = { 60 , 75 , 90 }

And , the measure of sides of ΔUVW = { 6 , 7.5 , 9 }

So , the scale factor of dilation is given by k

where k = measure of side ΔUVW / measure of side ΔXYZ

k = 6 / 60

k = 1/10

Hence , the dilation factor is k = 1/10

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Answer:

B. n - 6 ≥ 2; n ≥ 8

Step-by-step explanation:

A states that n minus 2 is greater than 6 - that's not what is stated in the problem. We can rule this out.

B states that n minus 6 is greater than or equal to 2. That's what we're looking for, now let's check it. If n is greater than or equal to 8, then it's true. Let's set n as 8. 8-6≥2 is correct!

C states that n plus 6 is greater than or equal to 2. We don't want addition, so rule it out.

D also states that n plus 6 is greater than or equal to 2. Again, no addition necessary, let's rule it out.

So, we're left with B as our correct answer!

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First, lets find the radius of the circle.

For a circle inscribed in a square, the diameter of this circle is equal to the side lenght.

D = 4.4

Since the radius (r) is D/2

r = 4.4/2 = 2.2

Now, we can calcule the area of the circle (A), using the following equation:

Answer:

The solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.

Step-by-step explanation:

To solve the equation 9 + 6/x = x + 10 for x, we can follow these steps:

Subtract 9 from both sides of the equation to isolate the 6/x term:

6/x = x + 1

Multiply both sides of the equation by x to eliminate the fraction:

6 = x^2 + x

Rearrange the equation into standard quadratic form:

x^2 + x - 6 = 0

Factor the quadratic:

(x + 3)(x - 2) = 0

Use the zero product property to find the solutions:

x + 3 = 0 or x - 2 = 0

x = -3 or x = 2

Therefore, the solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

$568.75.

Step-by-step explanation:

The value of the square root of 7 is,

⇒ √7 = 2.645

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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The question is missing some parts. Here is the complete question.

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost in type II ovens. A samplle of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with standar deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let \(\mu_{1}\) be the true mean repair cost for type I ovens and \(\mu_{2}\) be the true mean repair cost for type II ovens.

Step 1 of 4: State null and alternative hypothesis for the test.

Step 2 of 4: Compute the value of test statistics. Round your answer to 2 decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to 3 decimal places.

Step 4 of 4: Make the decision for the hypothesis test. (Reject or fail to reject Null Hypothesis)

Answer and Step-by-step explanation:

First, state null and alternative hypothesis:

\(H_{0}: \mu_{1}=\mu_{2}\)

\(H_{a}: \mu_{1}>\mu_{2}\)

Use z-statistics:

\(z = \frac{x_{1}-x_{2}}{y}\)

where x₁ and x₂ are the means and:

\(y=\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }\)

Calculating value of test stattistic:

\(y=\sqrt{\frac{(23.47)^{2}}{61}+\frac{75.25^{2}}{45} }\)

\(y = \sqrt{9.030+5.046}\)

\(y = \sqrt{14.076}\)

y = 3.752

\(z = \frac{79.6-75.25}{3.752}\)

z = 1.16

The test statistics is z = 1.16

The decision rule for rejecting null hypothesis is: \(\alpha\) ≤ test statistics

Using z-score table, it is possible to determine p-value, which is:

p-value = 0.877

Comparing p-value with level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.