A bicyclist travelled for T = 1.6 hours at a constant speed of R = 20 kilometers (km) per hour. Use the formula
D = R · T
to find the total distance traveled in kilometers.

Allison purchased lemons for $0.75 each.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is showing.

Now, Two point on the line are (4, 3) and (8. 6)

Hence, Equation of line is,

⇒ y - 3 = (6 - 3) / (8 - 4) (x - 4)

⇒ y - 3 = 3/4 (x - 4)

⇒ 4 (y - 3) = 3 (x - 4)

⇒ 4y - 12 = 3x - 12

⇒ 4y = 3x

⇒ y = 3/4x

⇒ y = 0.75x

Where, y is cost and x is number of lemons.

Hence, Allison purchased lemons for $0.75 each.

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The resulting values of the given operations are listed below.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given are various operations.

(1) 235,654 ÷ 10000

When dividing a number with any powers of 10, we will shift the decimal point from right to left up to the number of zeroes in the given power of 10.

Here 10,000 contains 4 zeroes.

235,654 can be written as 235,654.00.

Shift the decimal point 4 places from left to right.

235,654 ÷ 10000 = 23.5654 ≈ 23.57 rounded to two decimal places.

(2) 895,21 x 100

When multiplying a number with any powers of 10, we will shift the decimal point from left to right up to the number of zeroes in the given power of 10.

895,21 x 100 = 89521.00 x 100 = 895,2100

(3) 1307 in words is one thousand three hundred and seven.

(4) 1307 in expanded form.

1307 = (1 × 1000) + (3 × 100) + (0 × 10) + (7 × 1)

        = 1000 + 300 + 0 + 7

(5) 1307 + 13 = 1320

(6) In roman numerals, 1000 is M, 100 is C and 10 is X.

1320 = (1 × 1000) + (3 × 100) + (2 × 10) + (0 × 1)

        = M CCC XX

1320 in roman numerals is MCCCXX.

Hence all the operations are found.

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Answers:

=============================================

Explanation:

An exponential function has the template

y = a*b^x

where,

We have b = 1/4 = 0.25 as the base of the exponent.

Since 0 < b < 1 is the case, we have exponential decay

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

We can also have this template

y = a*(1+r)^x

I replaced b with 1+r

If we set this equal to 0.25 and solve for r, we get:

1+r = 0.25

r = 0.25-1

r = -0.75

The negative r value is another way to see how we have exponential decay

So we go from 1+r to 1+(-0.75) aka 1-0.75 as the base of the exponential.

In other words, 11600(0.25)^x is the same as 11600(1-0.75)^x

In the second format, it's much easier to see what the r value is.

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

The r value r = -0.75 converts to the percentage 75%

It means y decreases by 75% each time x goes up by 1.

Therefore , the solution of the given problem of domain comes out to be the appropriate domain for p(w) would be [1, 1000]

The domain of a function is the range of possible arguments that it can accept. The cross of the an f-like functional is represented by these numbers (x). The range of potential values to which a function can be applied is known as its domain. The value that the procedure returns after inserting the x value is part of this set. An equation for a function is Y = f, where y and x are predictor variables (x). When a given value of x can produce a single value of y, a parameter is said to be in the scope of a function.

Here,

Given :

1 kilogram to 1000 kilograms.

He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

So,

The appropriate domain for p(w) would be [1, 1000]

since

Aiden sells any amount of cumin seeds from 1 kilogram to 1000 kilograms.

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The complete question is "Aiden is a spice trader. He sells any amount of cumin seeds from 1 kilogram to 1000 kilograms. He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

p(w) models the price (in dollars) of w kilograms of cumin seeds in Aiden's shop. What's the appropriate domain?"

Answer:

68.1 square units

Step-by-step explanation:

l = Length of rectangle

 = 9 units

w = Width of rectangle

   = 6 units

The dashed lines represent the diameter of the circle. Semi-circle is exact half of a circle. This diameter is parallel to the width of the rectangle and is equal in measurement:

r = Radius of semi-circle

 = [tex]\frac{Diameter}{2}[/tex]

 = [tex]\frac{6}{2}[/tex] units

 = 3 units

∴Area of composite solid = Area of rectangle + Area of semi-circle

                                           = [(l × w) + [tex]\frac{1}{2}(\pi r^{2})[/tex]] [tex]units^{2}[/tex]

                                          = {[9 × 6] + [tex]\frac{1}{2}[\pi (3)^{2}][/tex]} [tex]units^{2}[/tex]

                                          = [54 + [tex]\frac{9}{2}\pi[/tex]] [tex]units^{2}[/tex]

                                          = 68.137 [tex]units^{2}[/tex]

                                         = 68.1 square units (Rounded to the nearest tenths place)

Answer:

y = 4x + 3

Step-by-step explanation:

See picture below :)

Answer:

17.24

Step-by-step explanation:

find the difference between 29 and 34. Then divide by 29 and multiply by 100. 34-29=5/29=0.1724 multiply by 100 =17.24%

Answer:

x = -3/5

Step-by-step explanation:

Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]

Solve for the variable x by isolating x-term, first move subtract both sides by 3x:

[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]

Subtract both sides by 9:

[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]

Therefore x = - 3/5

Answer:

x = -3/5 (or) x = -0.6

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 8x + 9 = 3x + 6

Then the value of x will be,

→ 8x + 9 = 3x + 6

→ 8x - 3x = 6 - 9

→ 5x = -3

→ x = -3 ÷ 5

→ [ x = -3/5 ]

Hence, the answer is -3/5.

Total snacks

15

Initially, cashews are 2x the amount of almonds

After 10 cashews are eaten, there are still 5 more cashews than almonds.

this gives us an insight into the amount eaten before they are equal

cashew eaten = 10

cashews left = almonds + 5

Therefore the almondds are 10 + 5 = 15

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The value of x for the given triangle will be 2.5. The correct option is B.

Geometry is defined as the branch in which we study the shapes like triangles, circles, cubes, rectangles, and squares and about their sides and area.

The similarity of the two shapes is defined as the sides of the two shapes being similar to each other irrespective of their size.

Here in the image, there are two triangles in a single figure and the two triangles are similar to each other.

The value of x will be calculated as:-

[tex]\dfrac{x}{2x + 5} = \dfrac{x-2}{2x -1 }[/tex]

2x² -x = 2x² + 5x - 4x - 5

-x = x - 5

-2x = -5

x = 2.5

Therefore, the value of x is 2.5 the correct option is B.

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On solving the provided question we can say that The average rate equation of change of g(x) from x = -3 to x = 3 is -27.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

Average Rate of Change = (g(b) - g(a)) / (b - a)

In this case, [tex]g(x) = -3x^3 + 3[/tex], and we need to find the average rate of change from x = -3 to x = 3.

So, we plug in the values of a=-3 and b=3 into the formula:

Average Rate of Change =[tex](g(3) - g(-3)) / (3 - (-3))[/tex]

[tex]= (-3(3)^3 + 3) - (-3(-3)^3 + 3)) / (6)\\= (-81 + 3) - (81 + 3)) / 6\\= (-78 - 84) / 6\\= -162 / 6\\= -27[/tex]

The average rate of change of g(x) from x = -3 to x = 3 is -27.

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The True Statement are:

20/21 of students in Manuel Class either walk or take bus to school.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have 2/7 of the students walk to school

and, 2/3 take the bus to school.

So, if both choices are considered

= 2/7 + 2/3

= 6/21 + 14/ 21

= 20/ 21

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All the probabilities are solved and are mentioned below.

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value

Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -

Pr(X = 0) = 0.55

Pr{X = 1) = 0.22

Pr(X = 2) = 0.13

Pr(X = 3) = 0.08

Pr(X = 4) = 0.02

We can find the probabilities as -

{ 1 } - the probability that two or fewer bits are transmitted in error :

P{E} = P(0) + P(1) + P(2)/∑P{n}

P{E} = 0.9/1

P{E} = 0.9

{ 2 } - the probability that at least one bit is transmitted in error -

P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}

P{E} = 0.45/1

P{E} = 0.45

{ 4 } - the expected value of the number of bits transmitted in error -

n = 0 + 1 + 2 + 3 + 4

n = 10

{ 4 } - the standard deviation of the number of bits transmitted in error -

σ = 1.0677

Therefore, all the probabilities are solved and are mentioned above.

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Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform a simple linear regression. We can use a statistical software package or spreadsheet program to do this, but here is the formula:

y = b0 + b1x

where:

y = price per share

x = annual dividend

b0 = y-intercept (constant)

b1 = slope (regression coefficient)

Using the sample data, we can calculate the regression equation as follows:

mean(x) = 9.8567

mean(y) = 53.0357

SSxx = Σ(x - mean(x))² = 7569.6844

SSxy = Σ(x - mean(x))(y - mean(y)) = 4542.4061

b1 = SSxy / SSxx = 4542.4061 / 7569.6844 = 0.6004

b0 = mean(y) - b1 * mean(x) = 53.0357 - 0.6004 * 9.8567 = 47.4759

Therefore, the regression equation is:

y = 47.4759 + 0.6004x

b. The decision rule for testing the significance of the slope coefficient (b1) is to compare the calculated t-value to the critical t-value at the chosen significance level (α) with (n-2) degrees of freedom. For this problem, we will use α = 0.05 and n = 30, so the degrees of freedom is 28. The null hypothesis is that the slope coefficient is equal to zero (i.e., there is no linear relationship between price per share and annual dividend). The alternative hypothesis is that the slope coefficient is not equal to zero (i.e., there is a linear relationship).

c. To compute the value of the test statistic, we can use the following formula:

t = b1 / (SEb1)

where:

SEb1 = standard error of the slope coefficient

SEb1 = sqrt(MSE / SSxx)

MSE = mean squared error

MSE = SSres / (n - 2)

SSres = residual sum of squares

Using the sample data, we can calculate the test statistic as follows:

SSres = Σ(y - ŷ)² = 583.8319

MSE = SSres / (n - 2) = 20.8518

SEb1 = sqrt(MSE / SSxx) = 0.0798

t = 0.6004 / 0.0798 = 7.526

d. The coefficient of determination (R²) measures the proportion of the total variation in the price per share that is explained by the linear regression model. We can calculate it using the following formula:

R² = SSreg / SStot

where:

SSreg = regression sum of squares

SSreg = b1² * SSxx

SStot = total sum of squares

SStot = Σ(y - mean(y))²

Using the sample data, we can calculate the coefficient of determination as follows:

SSreg = b1² * SSxx = 1707.4612

SStot = Σ(y - mean(y))² = 1866.6219

R² = SSreg / SStot = 0.9145

Therefore, 91.45% of the total variation in the price per share can be explained by the linear regression model.

(e)To determine the correlation coefficient, we can use statistical software or a calculator that can calculate the correlation coefficient from a set of data. Using a software or calculator, we get:

Correlation coefficient (r) = 0.7709

Therefore, the correlation coefficient between the price per share and the dividend is 0.7709. This indicates a strong positive correlation between these two variables.

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform linear regression analysis. We can use a statistical software or spreadsheet to do this. The results are:

Regression equation: price per share = 14.393 + 1.201(dividend)

Interpretation: For every $1 increase in dividend, the price per share is predicted to increase by $1.201, holding all other variables constant.

b. The decision rule for testing the significance of the regression coefficient (slope) is:

H0: β1 = 0 (the slope is not significantly different from 0)

Ha: β1 ≠ 0 (the slope is significantly different from 0)

Test statistic: t = (b1 - 0) / SE(b1)

Rejection region: t < -tα/2,n-2 or t > tα/2,n-2, where α = 0.05 and n-2 = 28 degrees of freedom

c. The value of the test statistic is:

t = (1.201 - 0) / 0.177 = 6.79 (rounded to two decimal places)

d. The coefficient of determination (R-squared) is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the explained variation to the total variation, and it ranges from 0 to 1. The formula is:

R-squared = explained variation / total variation

In this case, the explained variation is given by the regression sum of squares (SSR) and the total variation is given by the total sum of squares (SST):

SSR = Σ(y-hat - y-bar)^2 = 6418.95

SST = Σ(y - y-bar)^2 = 12345.44

Therefore, the coefficient of determination is:

R-squared = SSR / SST = 6418.95 / 12345.44 = 0.52 (rounded to two decimal places)

Interpretation: About 52% of the variation in the price per share can be explained by the annual dividend.

e. The correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship. The formula is:

r = cov(x,y) / (SD(x) * SD(y))

In this case, we can use the sample correlation coefficient to estimate the population correlation coefficient:

r = cov(price, dividend) / (SD(price) * SD(dividend))

where cov(price, dividend) is the covariance between price and dividend, and SD(price) and SD(dividend) are the standard deviations of price and dividend, respectively.

Using the formula or a spreadsheet, we get:

cov(price, dividend) = Σ[(price - mean price)*(dividend - mean dividend)] / (n - 1) = 417.25

SD(price) = 18.14

SD(dividend) = 6.10

Therefore, the correlation coefficient is:

r = 417.25 / (18.14 * 6.10) = 0.73 (rounded to two decimal places)

Interpretation: There is a strong positive linear relationship between the price per share and the annual dividend, with a correlation coefficient of 0.73.

An expression for e[z] by the given data is  E[z] = (n-1)/n * H_n-1.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_nT_{n+1} - T_n

for all positive integer values of n.

We are given that;

Balls are thrown uniformly and independently in all bins

Now,

We can express z as the sum of these binary random variables:

[tex]z = z_1 + z_2 + ... + z_{n-1}[/tex]

The random variables z_i are not independent, since the probability of throwing a ball into a bin that already has at least one ball in it depends on the number of balls already in the bin.

However, we can still use the linearity of expectation to calculate the expected value of z:

[tex]E[z] = E[z_1 + z_2 + ... + z_{n-1}][/tex]

By the linearity of expectation, we can distribute the expectation over the sum:

[tex]E[z] = E[z_1] + E[z_2] + ... + E[z_{n-1}][/tex]

Using these probabilities, we can calculate the expected value of each z_i:

[tex]E[z_i] = 1 * P(z_i=1) + 0 * P(z_i=0)= P(z_i=1)[/tex]

= (i-1)/n-i+1

Substituting this into the expression for E[z], we get:

[tex]E[z] = (1-1/n) + (2-1/n-1) + ... + (n-1-1/2)= (n-1)/n + (n-1)/n-1 + ... + 1/2[/tex]

This is a finite arithmetic series with n-1 terms, with first term (n-1)/n and common difference -1/n. Using the formula for the sum of an arithmetic series, we get:

[tex]E[z] = (n-1)/n + (n-2)/n + ... + 1/n= (n-1)/n * (1 + 1/2 + ... + 1/(n-1))[/tex]

This sum is known as the n-th harmonic number, denoted H_n.

Therefore, by arithmetic sequence the answer will be E[z] = (n-1)/n * H_n-1

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Answer:

D: [-4, ∞) and R: [0, ∞)

Step-by-step explanation:

The answer is D: [-4, ∞) and R: [0, ∞)

The price that dealerships pay for vehicles is called the wholesale price.

The sticker price of the car, given the MSRP and the navigation package among others, is $ 33, 699.

The sticker price of the car is the MSRP plus the price of any additional options or charges. So we need to add up the MSRP, premium package, navigation package, and destination charge:

Sticker price:

= MSRP + premium package + navigation package + destination charge

= 29, 999 + 2, 500 + 500 + 700

= $ 33,699

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The sum of their 3 prime numbers is 24.

Let's start by finding the prime numbers that Jimmy, Kimmy, and Timmy are thinking of.

We know that the product of Jimmy's and Kimmy's prime is 34. Since 34 is not a prime number, it must be the product of two prime factors.

The only way to factor 34 as a product of two primes is 2 x 17.

So we know that Jimmy's prime is either 2 or 17, and Kimmy's prime is the other one. We also know that Kimmy's and Timmy's primes multiply to 85. Again, 85 is not a prime number, so it must be the product of two prime factors.

The only way to factor 85 as a product of two primes is 5 x 17.

Therefore, we know that Timmy's prime is 5.

So the three primes are 2, 17, and 5.

The sum of these three primes is 2 + 17 + 5 = 24.

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Therefore , the solution of the given problem of test statistics comes out to be Using a z-table or calculator, we find the p-value to be approximately 0.0423.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the p-value for the this Z-value.

Here,

To test Aaron's claim, we can use a two-sample proportion z-test.

Let p1 be the proportion of cat persons in the Orlando population, and p2 be the proportion of cat persons in the rural population.

Null hypothesis: p1 = p2 (there is no significant difference in how appealing owning a cat is between city residents and rural residents)

Alternative hypothesis: p1 ≠ p2 (there is a significant difference in how appealing owning a cat is between city residents and rural residents)

We can use the following formula to calculate the test statistic:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where p is the pooled proportion, n1 and n2 are the sample sizes, and

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of cat persons in each sample.

Plugging in the values, we get:

p1 = 62/119 = 0.5210

p2 = 48/117 = 0.4103

n1 = 119, n2 = 117

p = (62 + 48) / (119 + 117) = 0.4661

z = (0.5210 - 0.4103) / sqrt(0.4661 * (1 - 0.4661) * (1/119 + 1/117)) ≈ 2.0296

Using a z-table or calculator, we find the p-value to be approximately 0.0423.

Since the p-value (0.0423) is less than the significance level (0.05), we reject the null hypothesis. We can conclude that there is a significant difference in how appealing owning a cat is between city residents and rural residents.

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The value of the variable(s) in the figure is  60°, explaination is given below.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that function at those values of the considered variables.

We are given that;

The variables; (5y)⁰,(2x)°,120⁰,1080

Now,

The first two expressions are both equal to 1, because any number raised to the power of 0 is always 1.

The third expression, 120°, is an angle measurement in degrees. In a triangle, the sum of the interior angles is always 180°. So, if we let x and y be the other two angles in the triangle, we have:

x + y + 120° = 180°

Simplifying this equation, we get:

x + y = 60°

Therefore, the answer of the given function will be  60°.

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hay 12, 6 pequeños que se pueden ver a simple vista y luego 6 que se puede formar con los demás

From the arithmetic sequence, the last row has 47 seats, and the auditorium has 15 rows.

We can solve this problem by recognizing that the number of seats in each row forms an arithmetic sequence. Let's call the first term of the sequence (the number of seats in the first row) "a" and the common difference between terms (the number of seats added for each subsequent row) "d".

Using this notation, we have:

a = 8

a + d = 11

a + 2d = 14

We can solve for a and d by subtracting the first equation from the second and the second equation from the third:

d = 3

a = 5

Therefore, the arithmetic sequence that describes the number of seats in each row is:

5, 8, 11, 14, ...

To find the number of seats in the last row, we need to find the nth term of this sequence, where n is the number of rows in the auditorium. We can use the formula for the nth term of an arithmetic sequence:

an = a + (n - 1)d

Since we don't know n, we need to find it first. We can use the formula for the sum of an arithmetic sequence to find the number of rows:

Sn = n/2(2a + (n - 1)d)

We know that there are 435 seats in total, so we can set Sn equal to 435 and solve for n:

435 = n/2(2(5) + (n - 1)(3))

435 = n/2(3n + 7)

870 = n(3n + 7)

3n^2 + 7n - 870 = 0

(n - 15)(3n + 58) = 0

Since n cannot be negative, we have n = 15.

Now that we know there are 15 rows, we can find the number of seats in the last row by plugging n = 15 into the formula for the nth term:

an = a + (n - 1)d

a15 = 5 + (15 - 1)(3)

a15 = 5 + 42

a15 = 47

Therefore, the last row has 47 seats, and the auditorium has 15 rows.

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Translation:

Inside an auditorium there are 435 seats, in such a way that in the first row there are 8 seats, in the second row there are 11, in the third there are 14, and so on, an arithmetic sequence is formed. How many chairs are in the last row? How many rows does that auditorium have?

Answer:

(g ￮ h)(t) = 8t

Step-by-step explanation:

to find (g ￮ h)(t) substitute t = h(t) into g(t)

(g ￮ h)(t)

= g(h(t))

= g(4t - 2)

= 2(4t - 2) + 4

= 8t - 4 + 4

= 8t

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Answer:

3.5841 x 10^7

Step-by-step explanation:

358.41 / 100

and add 2 powers of 10

Answer:

15. x = -3.

16. x = -2.

17 x = 2.

Step-by-step explanation:

To solve the equation 7x + 5 = 12x - 10, we want to isolate the variable x on one side of the equation. We can do this by adding or subtracting terms from both sides of the equation until we have x by itself.

First, let's simplify both sides of the equation by combining like terms:

7x + 5 = 12x - 10

-7x -7x (subtracting 7x from both sides)

5x + 5 = -10

Next, let's isolate the term with x by subtracting 5 from both sides of the equation:

5x + 5 = -10

-5 -5 (subtracting 5 from both sides)

5x = -15

Finally, let's solve for x by dividing both sides of the equation by 5:

5x = -15

x = -3

Therefore, the solution to the equation 7x + 5 = 12x - 10 is x = -3.

26 = 24 - x

-24 -24 (subtracting 24 from both sides)

2 = -x

Next, let's isolate the variable x by multiplying both sides of the equation by -1:

2 = -x

-1 -1 (multiplying both sides by -1)

-2 = x

Therefore, the solution to the equation 26 = 24 - x is x = -2.

2(6x - 7) = 10

12x - 14 = 10

Next, let's isolate the term with x by adding 14 to both sides of the equation:

12x - 14 = 10

+14 +14 (adding 14 to both sides)

12x = 24

Finally, let's solve for x by dividing both sides of the equation by 12:

12x = 24

x = 2

Therefore, the solution to the equation 2(6x - 7) = 10 is x = 2.

The inequality that represents the constraint faced by Leo in needing to score at least 83 points is 5 c + 8 a ≥ 83.

Let's first find the total number of computation and application problems that Leo needs to answer correctly to score at least 83 points on the test.

Let c be the number of computation problems that Leo answers correctly, and let a be the number of application problems that he answers correctly.

Total points is therefore :

= 5 c + 8 a

To maintain his B average, Leo needs to score at least 83 points on the test. Therefore, we can add the inequality part to make it:

5 c + 8 a ≥ 83

This shows that Leo needs to score either 83 points or above that in the test.

Find out more on inequalities at https://brainly.com/question/29184830

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