i thought of a number. 4 times my number increased by 30 equals 70 decreased by the number. what is my number

The missing side length for the triangle is given as follows:

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º on the triangle, we have that:

The tangent of 60º is equals to the square root of 3, hence the value of x is obtained as follows:

tan(60º) = 16/x

[tex]\sqrt{3} = \frac{16}{x}[/tex]

[tex]x = \frac{16}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The triangle is given by the image presented at the end of the answer.

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Answer:

x > -1

Step-by-step explanation:

8x - 4 > 3x - 9

5x - 4 > -9

5x > -5

x > -1

The answer is option A, pet ownership is the independent variable.

In experimental research, an independent variable is the variable that is manipulated by the researcher to determine its effect on the dependent variable. In this case, the independent variable is pet ownership, which is being studied to determine its effect on the health and lifespan of pet owners.

The dependent variable, in turn, is the health and lifespan of pet owners, which is expected to be influenced by their pet ownership status.

It is important to note that the relationship between pet ownership and health/lifespan could be influenced by other factors, such as age, income, or lifestyle. These other factors are known as spurious variables and can confound the relationship between the independent and dependent variables.

Operational variables, on the other hand, refer to how the researcher measures or manipulates the independent and dependent variables.

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The surface area of the prism is 264m²

A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism but the specific one we will be talking about here is triangular based prism.

The surface area of a prism is obtained by adding the area of the faces. Therefore surface area = 2B +ph

area of the base = 1/2 bh

= 1/2 × 6 × 8

= 1/2 × 48

= 24m²

using Pythagoras theorem, the hypotenuse of the triangle = √ 6²+8²

= √ 36+64

= √100 = 10m

perimeter of the base = 6+8+ 10

= 24m

Therefore SA = 2×24 + 24 × 9

= 48 + 216

= 264m²

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Answer:

Step-by-step explanation:

Answer:4/3

Answer:

The tangent of the larger acute angle in a right triangle with side lengths 10, 24, and 26 is 12/5.

Step-by-step explanation:

In a right triangle, the hypotenuse (the side opposite the right angle) is the longest side.

Therefore, in a right triangle with side lengths 10, 24, and 26, the hypotenuse measures 26 units and the legs measure 10 and 24 units.

In a right triangle:

Therefore, the largest acute angle is between the hypotenuse and the shortest leg, which means the side opposite the angle is the longest leg.

The tangent ratio is the ratio of the side opposite the angle to the side adjacent the angle.

Therefore the tangent of the largest acute angle is:

[tex]\implies \sf \dfrac{O}{A}=\dfrac{24}{10}=\dfrac{12}{5}[/tex]

the y-coordinate must be 7 in order for the point to lie on the line.

A line in the xy-plane passes through the origin and has a slope of 1/7. Point B (1, 7) lies on the line, as the slope of the line is calculated by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept. Since the line passes through the origin, the y-intercept is 0. This can be expressed as y = (1/7)x + 0

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The minimum number of people over age 32 they must include in their sample or sample size is equals to the 486.

In this question, we will use the margin of error of the 98% confidence interval for the population mean to determine the minimum sample size. We have to provide following informations for consumption of milk per week among people over age 32.

Mean = 3.1 liters

Confidence interval = 98%

Maximum/Margin of error = 0.1 liters

Standard deviations = 0.9 liters

level of significance, α = 1 - 0.98 = 0.02

or α/2 = 0.01

We have to determine the sample size for people over age 32 they must include in their sample. The margin of error is calculated by multiplying a key factor (for a certain level of confidence) by the population standard deviation. The result is then divided by the square root of the number of observations in the sample. Mathematically, [tex] ME =Z_{\frac{\alpha}{2}}\sqrt{ \frac{ σ}{n} }[/tex]

Using the Z-distribution table, value of z for 98% of confidence interval is 2.326. Substituting the known values in above formula, 0.1 = 2.326 √0.9/n

=> √0.9/n = 0.1/2.33 = 0.043

=> 0.9/n = (0.043)² = 0.001849

=> n = 0.9/0.00185

=> n = 486.4865 ~ 486

Hence, required sample size is 486.

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At steady state, the total WIP in the system is equal to the throughput time divided by the time it takes to make one loaf. Thus, the total WIP in the system is 3.5 loaves.

The total WIP in a system is the sum of all of the work that is in progress. At steady state, the total WIP in the system can be calculated by dividing the throughput time (the time it takes for one loaf to be processed from start to finish) by the time it takes to make one loaf.

In this example, the throughput time is 3 hours 30 minutes and it takes 1 hour to make one loaf. Therefore, the total WIP in the system is 3.5 loaves. This means that at any given time, there are 3.5 loaves in progress in the system.

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Answer: She has 10$ to save

Step-by-step explanation:

Elsia has 30$ to start her week. She spent 10 on food and drink, (30-10=20) 5 on entertainment, (20-5=15), and 5 on Misc. things. (15-5=10). This means that the answer is 10.

Steps:

30-10=20

20-5=15

15-5=10

I hope it helped! :D

Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Answer:

n=12

Step-by-step explanation:

sum of interior angles of polygon with n sides = (n-2)180

measure of an interior angle of a polygon times the number of sides (n) = sum of interior angles of polygon with n sides, therefore:

(n - 2)180 = 150n

180n - 360 = 150n

30n = 360

n = 360/30 = 12

The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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a) Michael's z-score is 1.83.

b) Josh's z-score is 2.

A z-score (also known as a standard score) is a statistical measurement that represents the number of standard deviations a data point is from the mean of the population. It's a way to standardize scores from different populations or datasets, allowing for easier comparisons.

To find the z-score, we use the formula

z = (x - μ) / σ

where

x = the individual score

μ = the mean of the population

σ = the standard deviation of the population

For Michael's score

x = 83

μ = 72

σ = 6

z = (83 - 72) / 6 = 1.83

Therefore, Michael's z-score is 1.83.

For Josh's score

x = 61

μ = 55

σ = 3

z = (61 - 55) / 3 = 2

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There are 105 ways to select a sample of 5 keyboards from a set of 10 keyboards such that exactly 2 of the keyboards have an electrical defect.

To find the number of ways to select a sample of 5 keyboards so that exactly 2 have an electrical defect, we can use the combination formula:

 C(n,k) = n! / (k! * (n-k)!)

where n is the total number of keyboards, k is the number of defective keyboards, and C(n,k) is the number of ways to choose k defective keyboards from a total of n keyboards. Here, n = 10 (assuming there are 10 keyboards in the sample), and k = 2.

We can choose 2 defective keyboards from the total of 3 defective keyboards in C(3,2) = 3 ways. We can also choose 3 non-defective keyboards from the total of 7 non-defective keyboards in C(7,3) = 35 ways. Therefore, the total number of ways to select a sample of 5 keyboards so that exactly 2 have an electrical defect is:

C(3,2) * C(7,3) = 3 * 35 = 105

So there are 105 ways to select a sample of 5 keyboards from a set of 10 keyboards such that exactly 2 of the keyboards have an electrical defect.

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The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

(3.1x + 2.8z) - (4.3x - 1.2z)

open parenthesis

3.1x + 2.8z - 4.3x + 1.2z

combine like terms

3.1x - 4.3x + 2.8z + 1.2z

-1.2x + 4x

Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.

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Answer: If Ava sells a $365 laptop, then she will make $91.25 in commissions.

Step-by-step explanation: 25% of 365 is 91.25

The area οf the sectοr bοunded by a 180 degrees arc with a radius οf 6 inches is 18π square inches.

The area οf a sectοr bοunded by a central angle θ and radius r is given by the fοrmula:

A = (θ/360) x πr²

In this case, the central angle is 180 degrees and the radius is 6 inches.  we get:

A = (180/360) x π(6²)

= (1/2) x π x 36

= 18π

Therefοre, the area οf the sectοr bοunded by a 180 degrees arc with a radius οf 6 inches is 18π square inches.

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A multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor A and three levels for factor B can be written as:

Y = b0 + b1A + b2B + b3AB + e

where Y is the dependent variable, A is the independent variable for factor A, B is the independent variable for factor B, A*B is the interaction between A and B, and e is the error term.

The variables can be defined as follows:

Y: The dependent variable that is being measured in the study.

A: The independent variable representing factor A, which has two levels (A1 and A2).

B: The independent variable representing factor B, which has three levels (B1, B2, and B3).

A*B: The interaction term between factor A and factor B.

e: The error term that captures the variability in the dependent variable that is not explained by the independent variables.

This equation allows us to examine the main effects of both factors (A and B) as well as their interaction (A*B) on the dependent variable Y in a two-factorial design.

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Answer:

The function h(t) = -16t^2 + 112t + 60 is a quadratic function, which means it is defined for all real numbers.

Therefore, the domain of h(t) is the set of all real numbers. In interval notation, we can express this as:

Domain of h(t): (-∞, ∞)

Answer:

Step-by-step explanation:

To solve this question, we can use the formula for compound interest:

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

Where:

A is the total amount of money after t years

P is the initial principal (in this case, $600)

r is the annual interest rate (4%)

n is the number of times the interest is compounded per year (12, for monthly compounding)

t is the number of years

Plugging in the values, we get:

A = 600(1 + 0.04/12)^(12*14)

A = 600(1.00333)^168

A = $988.42 (rounded to two decimal places)

So, after 14 years, Levi will have approximately $988.42 in his account.

Answer:

4

Step-by-step explanation:

4+6=10

Answer:

In this problem, we have a right triangle where the hypotenuse is the 30-foot support cable and one leg is 22 feet (the distance from the base of the pole to where the cable is attached). To find the angle that the cable makes with the ground, we need to use trigonometry. The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, we want to find tan(θ), where θ is the angle between the cable and the ground. Therefore, tan(θ) = opposite/adjacent = 22/30 = 0.7333. Taking inverse tangent on both sides gives us θ = tan^-1(0.7333) ≈ 36.7 degrees to one decimal place. Therefore, to the nearest tenth, the measure of the angle that the cable makes with the ground is approximately 36.7 degrees.

Answer:

Step-by-step explanation:

To find out how many people in the United States did not live in Texas in 1900, we can subtract the population of Texas from the population of the United States:

Number of people in the United States who did not live in Texas = Population of the United States - Population of Texas

Number of people in the United States who did not live in Texas = 76.1 million - 3.05 million

Number of people in the United States who did not live in Texas = 73.05 million

Therefore, about 73.05 million people in the United States did not live in Texas in 1900.

Answer: 73.05 million people in the United States did not live in Texas in 1900.

Step-by-step explanation:

The ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one according to the one's place of 8 and 9 powers.

Here, we need to find the unit digit of [tex]1998^{1999}[/tex] :

8 power of any dight will give us the unit digit of 8, 4, 2 and 6.

Here 8 has power 9.

Then the unit place of the sum will be equal to 2.

Similarly, we need to find the sum of other one.

Other sum: [tex]1999^{1998}[/tex]

9 power of 8

9 power of odd numbers will give 9 as unit digit.

9 power of even numbers will give 1 as unit digit.

Here, we have 8 as power the, we will get the unit digit as 1.

Now we need to simplify the sum.

Unit digit of  [tex]1998^{1999}-1999^{1998}[/tex] is equal to 2 - 1 = 1.

The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one.

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The 1s in 14.937 and 6.1225 have distinct values. The digit 1 in 14.937 is in the thousandths place, representing a value of 0.001, but the digit 1 in 6.1225 is in the hundredths place, representing a value of 0.01.

When we compare the values of the 1s in these two numbers, we can observe that the 1 in 6.1225 is 10 times bigger than the 1 in 14.937. This is due to the fact that the place value of digit 1 in 6.1225 is ten times bigger than the place value of digit 1 in 14.937. It should be noted that while comparing the values of digits in numbers, their location or place value is a significant consideration. Even the smallest Changes in a digit's location can have a substantial influence on its total value. The variation in place value of the 1s in 14.937 and 6.1225 leads in a considerable disparity in their respective values in this situation.

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The length of the altitude drawn to the hypothenuse, WY as required to be determined is; 6.

As evident from the task content, it follows that the length of the altitude, WY drawn to the hypothenuse is to be determined.

Let WY be represented as a;

By observation; it follows that the triangles WXY and WXY are similar triangles.

Hence, the ratio which holds in the figure is;

12 / a = a / 3

Therefore by cross-multiplication, we have that;

a² = 36

a = 6.

Ultimately, the length of the altitude drawn to the hypothenuse is; 6.

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The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.

This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.

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When the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction is four times the value of the numerator

The denominator of a certain fraction is a number that divides the numerator to produce a fraction. The fraction has two parts, the numerator, and the denominator. The numerator is the top part of a fraction, and the denominator is the bottom part of the fraction. When the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction can be calculated using a mathematical formula.

The mathematical formula for calculating the value of the denominator of a certain fraction is to divide the numerator by the quarter. This is because the numerator is a quarter of the value of the whole fraction. Therefore, the formula is represented as:D = N/1/4where D is the denominator, and N is the numerator of the fraction.To solve for D, we multiply both sides by the reciprocal of the fraction:1/4 = 4/1, so we have:D = N x 4/1D = 4N/

Therefore, the value of the denominator of the fraction is four times the value of the numerator. If the numerator of the fraction is 2, then the denominator of the fraction is 8. In summary, when the numerator of a certain fraction is a quarter of the value of the whole fraction, the value of the denominator of that fraction is four times the value of the numerator.

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The critical value to be used in conducting a Lagrange multiplier test for second-order autocorrelation at the five-percent level of significance is 3.84.

The Lagrange multiplier test is a technique for testing hypotheses concerning the existence of structure in the disturbance term of regression models. In a variety of econometric models, the presence of autocorrelation (serial correlation) and heteroscedasticity are two examples of such structures.

The LM test is used to determine whether or not autocorrelation is present in a regression model, with the null hypothesis being that there is no autocorrelation. The null hypothesis is always of the form that there is no structure in the disturbance term, i.e. that the errors are not autocorrelated, and the alternative hypothesis is always of the form that some or all of the coefficients are nonzero, indicating the presence of autocorrelation or heteroscedasticity.

The critical value for the Lagrange multiplier test is calculated using a chi-squared distribution, with the degree of freedom being equal to the number of coefficients tested.

The formula for the Lagrange multiplier statistic is given:

LM = T * R² where T is the sample size and R² is the coefficient of determination for the regression.

This value is compared to the critical value of the chi-squared distribution with one degree of freedom to determine whether or not to reject the null hypothesis of no autocorrelation.

The level of significance of the test determines which critical value to use. In this case, the level of significance is 5 percent, so the critical value is 3.84.

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