A pet store is selling dogs for $140 and cats for $70. If 28 pets were sold and the
receipts were $3360, how many cats were sold?

The volume of a cube is given by the formula V = s^3, where s is the length of one of its sides. So, if the edge length of a cube is 3 inches, its volume would be:

V = 3^3 = 27 cubic inches

we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.

likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}\)

\(\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}\)

Numbers greater than zero but less than one have squares that are smaller.

Consider the number one-half (1/2); half of a half is a quarter (1/4 < 1/2)!

Of course, the square of a negative number is greater (since a negative squared is positive).

Only the numbers zero and one are equal to their squares.

another explanation:

Yes .

In fact there is an infinite number of numbers that have that condition. For example (1/2)² = 1/4.

In fact any positive number ’n’ such that 0<n<1 is a number which has a smaller number when squared.

Answer:

20 hours

Step-by-step explanation:

first calculate volume:

12x10x3=360

then divide by 18

360/18=20

So 20 hours in total

Answer:

(6^-4)^-4, (6^-2)^-8, (6^8)^2

The expressions are equivalent to the given expression are (6²)⁸ and (6⁻⁴)⁻⁴. Therefore, options C and F are the correct answers.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 6¹⁶.

Here, 6¹⁶=(6⁴)⁴

6¹⁶=(6²)⁸

6¹⁶=(6⁸)²

6¹⁶=(6⁻⁴)⁻⁴

Therefore, options C and F are the correct answers.

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Answer:

  g. x = -3, 1.875

  h. (-3, 1.875)

Step-by-step explanation:

You want the solutions to K(x) = -6 for K(x) -1.6x² -1.8x +3, and the interval for which K(x) > -6.

The attached graph shows K(x) = -6 for x = -3 and x = 1.875.

The attached graph shows K(x) > -6 between the above values, on the interval (-3, 1.875).

__

Additional comment

We are grateful that we are directed to use technology on this problem, as a graphing calculator makes answering these questions so much easier.

Answer:

the actual sales be $31,132

Step-by-step explanation:

The computation of the actual sales is as follows:

Let us suppose the actual sales be x

Now the sales tax be 0.06x

Now the total sales would be

x + 0.06x = $33,000

1.06x = $33,000

x = $33,000 ÷ 1.06

= $31,132

hence, the actual sales be $31,132

The same is to be considered by applying the above equation

Answer:

actual sales be $31,132

Step-by-step explanation:

Answer:

i think maybe j that is what I think

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

Step-by-step explanation:

We need to write our function in the formula for Exponential Decay a(1-r)^x  

We can represent "a" in our equation as the original sample size for the substance (800 mg).

According to the formula, we need to subtract our rate of decay from 1. Remember! We CANNOT use the percent's decimal as a number. We need to convert the percent to a decimal. We do this by moving the decimal place backwards 2 places. 7.2% = .072

1 - .072 = .28

Now we have the equation f(x) = 800(0.28). But where are the variables? That is our next problem. If t is the number of years since 2001, then we need to multiply it by the rate of decay (.28t). Now there is only one variable left, which is y.
Our answer is f(x) = 800(.28t)^y

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

Answer:  5

Step-by-step explanation:

3(2x-3)=21

6x-9=21

6x=30

x=5

Answer:

\( k(x - 2)(x - 7) = 0 \)

Step-by-step explanation:

Since x = 2, and x = 7 are both solutions to a quadratic equation, it implies that:

\( (x - 2) and (x - 7) \) are factors of the equation where k is included as a constant multiplying both factors.

Therefore, the equation would be as follows:

\( k(x - 2)(x - 7) = 0 \)

Answer:

k(x-2)(x-7)=0

Step-by-step explanation:

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer:

1 9/10

Step-by-step explanation:

Rewriting our equation with parts separated

1+1/2+2/5

Solving the fraction parts

1/2+2/5=?

Find the LCD of 1/2 and 2/5 and rewrite to solve with the equivalent fractions.

LCD = 10

5/10+4/10=9/10

Combining the whole and fraction parts

1+9/10= 1 9/10

OR

Solution by Formulas

Convert any mixed numbers to fractions.

Then your initial equation becomes:

3/2+2/5

Applying the fractions formula for addition,

(3×5)+(2×2)

      2×5

= 15+4

     10

= 19/10

Simplifying 19/10, the answer is

1 9/10

Hope this helps!

To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.

To find the length side we will use the following formula:

Where ap is the length of the apothem, and I is the side length.

Substituting the given values, we get:

Solving the equation for I, we get:

Therefore, the perimeter of the hexagon is:

Answer:

Answer:

2.25

Step-by-step explanation:

8.5-6.25

(8-6)+(0.5-0.25)

2+0.25

2.25

Answer:

2.25 or 9/4 is the answer

Hope this helps

An exponential expression with base 25 and a single, simplified exponent is \((25)^{-28}\)

In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

Generally speaking, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number, we have the following:

\((25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}\)

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Answer:

m = -2

Step-by-step explanation:

-m^3 + 17m + 44 = -(m + 2)(m^2 - 2m - 22)

m + 2 = 0 or m^2 - 2m - 22 = 0

m = -2 or m = 1 ± √23

Answer:C

Step-by-step explanation:

A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation

Answer:

C) strong negative.

Step-by-step explanation:

Tiled floor with 225 square tiles means the area of the square room is 225.

Formula needed: A = (side)^2 or in short

A = s^2.

We need to find s.

225 = r^2

sqrt{225} = sqrt{r^2}

15 = r

There are 15 tiles are along an edge of the room.

Answer:

Step-by-step explanation:

Answer:

i think 4 but im not 100% sure

Step-by-step explanation:

Answer:

8 i guess

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

5x2 is 10 and 10x4=40

Answer:

Y=2x-2

Step-by-step explanation:

Slope intercept form is also known as y=mx+b

The slope of a line is rise over run. In this case that would be 2/1 which simplifies to 2

The intercept is where the line crosses the y axis, which is at -2

So your equation would be y=2x-2

The buoyant force is the upward force on an object submerged in a fluid that is caused by the fluid's pressure.

The magnitude of the buoyant force is equal to the weight of the displaced fluid. Therefore, the correct ranking of the three buoyant forces is fx > fy > fz.

The magnitude of the buoyant force can be calculated using the equation Fb = ρgV, where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the displaced fluid. For orientation x, the buoyant force fx will be the greatest since the volume of the displaced fluid is the greatest. For orientation y, the buoyant force fy will be the second greatest since the volume of the displaced fluid is second greatest. Finally, for orientation z, the buoyant force fz will be the least since the volume of the displaced fluid is the least.

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