Jessie enjoys running every day for exercise. On Monday, he ran 3.30 miles. On Tuesday, he ran 3.09 miles. On Wednesday, he ran 2.98 miles. On what day did Jessie run the farthest? *

Answer:

QR and ST

Explanation:its right

Answer:

False

Step-by-step explanation:

Your answer is false because the 3 in 157.83 is in the hundereths place not the tenths place.

I hope it helps! Have a great day!

Lilac~

As the given equation is (36)ˣ⁺²  = 6 , then the solution for the given equation is x ≈ -1.54.

The given equation in the question is (36)ˣ⁺²  = 6

according to the given equation , the goal is to solve the equation for x.

For solving this equation ,

we'll have to use logarithmic operations which is as follows:  

log36(6) = x+2.

We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.

Now, By subtracting 2 from both sides, we will get the value of x as:

x ≈ -1.54.

When we round off this value to the nearest 100th, we will get  -1.54.

Thus , the solution for the given equation is x ≈ -1.54.

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Answer:

b .3

Step-by-step explanation:

every thing else is even and if u add them up u will get to 32 eventually

Answer:

B.) 3

Step-by-step explanation:

To do this problem, we should find out what factors can equal 32. So let's start with finding out. This problem is going to require multiplication and division.

Letter A is a multiple of 32, because:

32 ÷ 2 = 16, which means that 16 x 2 = 32.

Because 2 can be divided equally into 32, this answer is wrong.

_________________

Letter C is a multiple of 32, because:

32 ÷ 4 = 8, which means that 8 x 4 = 32.

Because 4 can be divided equally into 32, this answer is also wrong.

_________________

And, because the last answer equaled 8, that means that:

32 ÷ 8 = 4, which means that 4 x 8 = 32.

Which is also wrong.

_________________

This leaves us with 32 ÷ 3 = 10.6666666667. This answer cannot be multiplied evenly into 32, so it is correct.

I hope that this helps.

x = 2

5(2 • 2 - 6) + 20

5(2x - 6 )+ 20 = 10

10x - 30 + 20 = 10

10x - 10 = 10

+10 +10

10 / 10x = 20 / 10

x = 2

Answer:

a. \(z_{1} = \frac{3\sqrt{2}}{2}+j\cdot 3\frac{\sqrt{2}}{2}\), b. \(z_{3} = -j\cdot 2\), c. \(z_{4} = -j\), d. \(z_{5} = 1\)

Step-by-step explanation:

All given complex numbers are in polar form, which are characterized by:

\(z = r\cdot e^{j\cdot \theta}\)

Where:

\(r\) - Magnitude, dimensionless.

\(\theta\) - Direction, measured in radians.

The rectangular form of complex numbers is represented by:

\(z = r\cdot (\cos \theta + j\cdot \sin \theta)\)

Now, each complex number is evaluated:

a. \(z_{1} = 3\cdot e^{j\cdot \frac{ \pi}{4} }\)

\(r = 3\) and \(\theta = \frac{\pi}{4}\)

\(z_{1} = 3\cdot \left(\cos \frac{\pi}{4}+j\cdot \sin \frac{\pi}{4} \right)\)

\(z_{1} = \frac{3\sqrt{2}}{2}+j\cdot 3\frac{\sqrt{2}}{2}\)

b. \(z_{3} = 2\cdot e^{-j\cdot \frac{\pi}{2} }\)

\(r = 2\) and \(\theta = -\frac{\pi}{2}\)

\(z_{3} = 2\cdot \left[\cos \left(-\frac{\pi}{2}\right) + j\cdot \sin \left(-\frac{\pi}{2} \right) \right]\)

\(z_{3} = -j\cdot 2\)

c. \(z_{4} = j^{3}\)

By definition of complex number, \(j = \sqrt{-1}\), which means that \(j^{2} = -1\). Hence:

\(z_{4} = j^{2+1}\)

\(z_{4} = j^{2}\cdot j\)

\(z_{4} = j\cdot j^{2}\)

\(z_{4} = -j\)

d. \(z_{5} = j^{-4}\)

By definition of complex number, \(j = \sqrt{-1}\), which means that \(j^{2} = -1\).

Hence:

\(z_{5} = \frac{1}{j^{4}}\)

\(z_{5} = \frac{1}{j^{2+2}}\)

\(z_{5} = \frac{1}{j^{2}\cdot j^{2}}\)

\(z_{5} = \frac{1}{(-1)\cdot (-1)}\)

\(z_{5} = 1\)

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3

Linear sequence is a sequence of number in order with same difference .or same ratio.

when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.

The sequence in the given question

-5 , -2 , 1 , 4 , 7, . . . .

The first term of sequence : a₁ = -5

The second term : a₂ = -2

Common difference : d = a₂ - a₁

=> d = -2 - (-5)

=> d = -2 + 5

=> d = 3

The nth rule of linear sequence is aₙ = aₙ₋₁ + d

replacing the value of d

aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.

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ANSWER

My answer is in the photo above

Answer:

1

Step-by-step explanation:

There are 2 categories male and female and 1 attribute those who text during driving so the number of cells is 2*1= 2

And degrees of freedom is found by subtracting 1 from k= k-1= 2-1= 1 where k is the number of the categories

The degrees of freedom for this chi square test of proportions is 1

The critical value for ∝= 0.05 is .χ²≥ χ²(0.05,1)= 3.84

The critical value for ∝= 0.01 is .χ²≥ χ²(0.05,1)= 2.71

The Fuel efficiency rate in miles per gallon is;  104.67 MPG

Let the initial amount of gallons be x

Now, after driving for 263 miles, you have 11 gallons of gas left in your tank.

Now, you continue driving and after driving 314 miles, you have 8 gallons left. This means that number of gallons used to drive 314 miles = 11 - 8 = 3 gallons

Therefore the Fuel efficiency rate which is in miles per gallon is;

MPG = 314/3

MPG = 104.67 MPG

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If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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The value of length m is 2.13cm

In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

therefore m² = k²+l²+2klCos M

m² = 4.4²+3.1²+ 2× 3.1×4.4cos 150

m² = 19.36+9.61+27.28(-0.8660)

m² = 28.97-23.62

m² = 5.35

m = √5.35

m = 2.31 cm( nearest tenth)

Therefore the measure of length m is 2.31 cm

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Answer:

Step-by-step explanation:

We know that the cosine of an angle is the reciprocal of the secant of the same angle, and the cotangent of an angle is the reciprocal of the tangent of the same angle. Therefore, we can use these relationships to find the value of the secant of an angle when the cotangent of the same angle is given.We are given that cot(o) = 13/6. Using the definition of the cotangent function, we know that:cot(o) = adjacent side / opposite sideWe can use the Pythagorean theorem to find the hypotenuse of a right triangle with adjacent side 13 and opposite side 6:h^2 = 13^2 + 6^2

h^2 = 169 + 36

h^2 = 205

h = sqrt(205)Now we can use the definitions of the secant and cosine functions to find the value of sec(o):sec(o) = hypotenuse / adjacent side

sec(o) = sqrt(205) / 13Therefore, the value of sec(o) is:sec(o) = sqrt(205) / 13 ≈ 1.5276

Answer:

146/x^23

Step-by-step explanation:

Answer:

A. 1.5 seconds

B. 36 feet

C. 0 feet

D. After 3 seconds

Step-by-step explanation:

I graphed it on desmos.

if M > N then the inequality M/N > N/M will be always true

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

As in the question M is always greater N

So, is M is divided by a number that is less than M the answer will always be greater than 1

but on the other hand, if N is divided by a number greater than N then the answer will always be less than 1

Therefore, M/N > N/M will always be True

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Answer:

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Step-by-step explanation:

The critical value for one tailed test is t ∝(7) > 1.895

A one tailed test is performed to test the claim that advertisements were viewed more in the morning (before noon) or in the evening (after 5pm)

The null and alternative hypotheses are

H0: μm = μe   vs     Ha μm > μe

where μm is the mean of the morning and μe is the mean of evening.

The calculated value of t = -1.152587077  which is less than the critical region hence the null hypothesis cannot be rejected .

P(T<=t) one-tail 0.143458126 > 0.05

If two tailed test is performed the critical region is t Critical two-tail 2.364624252

and the calculated t value is  -1.152587077  which again does not lie in the critical region .

Hence μm =  μe or    μm ≤ μe

P(T<=t) two-tail 0.286916252  > 0.025

Therefore

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Option b gives the best answer.

Answer:

The choice b.

\( \sin \: A = \frac{4}{5} \)

Step-by-step explanation:

sinA = opposite/hypotenuse

\(sinA = \frac{28}{35} = \frac{4}{5} \)

Answer:

$172,984.44

Step-by-step explanation:

We can use the formula

\(A = P(1 + \frac{r}{n})^{nt}\) to compute the final amount

Here P is the principal amount, the original deposit = $25,000

r is the annual interest rate = 6.5% = 0.065 in decimal

n is the number of times the compounding takes place. Here it is quarterly so it is 4 times a year

t is the number of time periods ie 30 years

A is the accrued amount ie principal + interest

Computing different components,

\(nt = 4 \times 30 = 120\)

\(r/n = 0.065/4 = .01625\)

\(1 + r/n = 1.01625\)

\((1 + r/n)^{nt} = 1.01625^{120}\)

Therefore

\(A = 25000 \times 1.0625^{120} = 172,984.44\)

Answer:

You will have $172,984.44

Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)

Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.

In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.

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Answer:

Step-by-step explanation:

Given function:

\(y=\sqrt{x-2}\)

The domain is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, the domain of the given function is restricted.

\(x-2\geq 0 \implies x\geq 2\)

Therefore, the domain of the given function is [2, ∞).

The range is the set of all possible output values (y-values).

As the square root of a negative number cannot be taken, the range of the given function is restricted.  

Therefore, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value \(c\) in its domain:

\(\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}\)

Therefore, the function is continuous on its domain [2, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

\(\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}\)

Therefore, there are no stationary points.

As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).

\(\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0\)

\(\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0\)

Increasing

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}\)

Decreasing

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}\)

Therefore:

\(\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}\)

\(\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}\)

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: [2, ∞)

Range: [0, ∞)

Continuity: Function is continuous on its domain [2, ∞).

Minimum point at (2, 0).

Increasing function: (2, ∞)

Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.

The probabilities in these cases are 0.125, 0.375, 0.58, 0.16, 0.5  and the only prime and even number is 2.

The probability is defined by the formula: specific outcome/ total possible outcomes. Based on this, let's calculate the probability in each case:

A prime number can be defined as a number that can be divided only by 1 and the number itself. On the opposite, a composite number can be divided by at least another number than 1 and itself.

The only prime and even number is 2.

Note: Here is the question in English:

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Answer:

45

Step-by-step explanation:

Answer:

"c" OPTION IS CORRECT

Step-by-step explanation:

At last you will get result if you solve it for x,

x>3.5

Answer:

3/5 is larger.

Step-by-step explanation:

To figure this out, you need to divide 3 by 5. Your answer should be 0.6. Now that they're both decimals, you can clearly see that 3/5 is larger because 0.6 > 0.41. The trick is don't look at the 1 at the end of .41. Just compare .6 with .4. Which is larger 6 or 4? If you guessed 6, you are correct!

Answer:

4*9

Step-by-step explanation:

It's obvious.

Step-by-step explanation:

The domain tells us the possible x values in a function.

Look at the function, it has a open circle at x=-4 and it has a closed circle at x=6. This means that we can any value of number that is between negative 4 and 6. It cannot be negative 4 since it has a open circle so our domain is

\( - 4 < x \leqslant 6\)

The range is possible y values. Looking at the function, the lowest y value is at y=-3 and it has a open circle,

the highest y value is 3 and it at a closed circle.

This means we can have any y value from -3 and 3 but not -3 since it at a open circle so our range is

\( - 3 < y \leqslant 3\)