A, B, C and D are junctions on a motorway.

A B C D

distance CD= 3 x distance AB
distance BC= 25 miles

Salma drives from A to C.
She drives for 30 minutes at an average speed of 62 miles per hour.

Work out the distance AD.

Not drawn
accurately

Answer:

y = 13x + 86

Step-by-step explanation:

y−8 =13(x+6); distribute the 13

y - 8 = 13x + 78; now add 8 to both sides

y = 13x + 86; this is the slope intercept form

Answer:

23,023 minutes

Step-by-step explanation:

$45/20 = $2.25 in a minute

$51, 802/ 2.25 = 23,023 minutes

Answer:

i dont now..............................

Step-by-step explanation:

We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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The domain of the function is `R` and the y-intercept is `(0, -3)`

Given, `y = log4(2x + 1) - 3`.

To determine the domain of the function,

we should look for all values of `x` that would make the given function undefined.

There are no real values of `x` that would make the function undefined.

Therefore, the domain of the function is all real numbers or `R`.

To determine the y-intercept, substitute `x = 0` in the given function.`

y = log4(2(0) + 1) - 3 = log4(1) - 3 = 0 - 3 = -3`

Therefore, the y-intercept of the function is `(0, -3)`.

Hence, the domain of the function is `R` and the y-intercept is `(0, -3)`.

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Answer: 0.88 should be the answer

Answer:

-5, -8 and-3, -3, -2

Step-by-step explanation:

4, -8, -3, 2.

2a.

I assume the "current value" means add up the cards in your hand

4-8-3+2= -5

2b.

You can remove negative number cards to increase score!

That would be -8 and -3 cards.

3c.

If you can only remove one card, and your current hand is -5, lets see..

by removing a card, you subtract its value, so

-5-4 = -9, thats not good

-5-(-8) = 3, thats kind of close to zero

-5-(-3) = -2, thats pretty close to zero!

-5-2 = -7, that's not good

The closest to zero we can get is by removing the -3 card, for which our hand will have the value -2.

Answer:

The answer should be (1,-2)

Step-by-step explanation:

because 4x1/4=1 and -8x1/4=-2 just divided and the answer will be (1,-2)

Answer:

Ankur found that the quotient of a positive number and a negative number is negative

Step-by-step explanation:

Given that:

Quotient of 15 and one-third divided by (negative 4 and two-thirds) = 3

Mathematically,

( 15 1/3) ÷ (-4 2/3) = 3

Here,

Dividend = 15 1/3 (positive)

Divisor = - 4 2/3 (negative)

Dividing a positive Dividend by a negative Divisor will always give a negative quotient

Hence,

15 1/3 = 46 / 3

-4 2/3 = - 14 / 3

46/3 ÷ - 14/3

= 46/3 * -3 / 14

Ankur must have either forgotten or neglected the negative sign in the divisor

The correct option which describes Ankur's error is: Ankur found that the quotient of a positive number and a negative number is positive.

Given that,

Ankur estimated the quotient of 15 and one-third divided by (negative 4 and two-thirds) = 3

We have to find,

Which best describes his error?

According to the question,

The two \(15\dfrac{1}{3}\) and \(-4\dfrac{2}{3}\) number are mixed fractions.

Ankur estimated the quotient of 15 and one-third divided by (negative 4 and two-thirds) = 3

Then,

Convert the equation into an improper fraction,

\(= \rm \dfrac{15\dfrac{1}{3}}{-4\dfrac{2}{3}} \\\\\ Convert \ into \ improper \ fraction\\\\= \dfrac{\dfrac{15\times3+1}{3}}{\dfrac{-4\times 3+2}{3}} \\\\\)

Now simplify the equation,

\(= \dfrac{\dfrac{46}{3}}{\dfrac{-10}{3}} \\\\\\ = \dfrac{\dfrac{46}{3} } {\dfrac{3}{-10}} \\\\\\ = \dfrac{-3}{14}\)

The mistake he has committed, while dividing two fractions, he must have forgotten that one of the fractions which is in the denominator bears a negative sign before it.

Ankur forgot to put the negative sign before 3.

Hence, The correct option which describes Ankur's error is: Ankur found that the quotient of a positive number and a negative number is positive.

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The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale

Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.

Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.

The formula for calculating the magnitude of an earthquake based on its amplitude is:

Magnitude = log10 (Amplitude) - 3

where the amplitude is measured in microns.

Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:

Magnitude = log10 (100,000) - 3

Magnitude = 5 - 3

Magnitude = 2

Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

Answer:

A). Scale factor = \(\frac{1}{4}\)

B). Length of the unknown side = 2.75 feet

Step-by-step explanation:

Part A

Since, the large rectangle was scaled by a scale factor 'k' to form the smaller rectangle,

Scale factor = \(\frac{\text{Side length of the image}}{\text{Side length of the preimage}}\)

                    = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

                    = \(\frac{4}{16}\)

                    = \(\frac{1}{4}\)

Part B

Scale factor = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

\(\frac{1}{4}=\frac{\text{Side length of the smaller rectangle}}{11}\)

Therefore, side length of the unknown side = \(\frac{11}{4}\) = 2.75 feet

Answer:

98,100,A

Plz mark me brainliest.

Step-by-step explanation:

The difference between the two expressions:

2x^5 and (2x)^5

Is the coefficient that multiplies the variable.

We want to see how the expressions:

2x^5 and (2x)^5

Are different.

Remember that the exponents can be distributed, then we can write the rule:

(a*b)^n = (a^n)*(b^n)

Then we can rewrite the second expression as:

(2x)^5 = (2^5)*x^5 = (2*2*2*2*2)*x^5 = 32x^5

So the difference between the two expressions is the coefficient that is multiplying the variable x.

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Answer: 2 1/5 partes  de torta

Step-by-step explanation:

Para contestar esta pregunta debemos sumar cada parte de torta:

0.7+9/12+6/8 =

Convertimos las fracciones en decimales, para tener todos los valores expresados de la misma forma. Dividiendo:

9/12=0.75

6/8=0.75

Sumamos :

0.7+0.75+0.75 = 2.2 partes = 2 1/5 partes

En conclusión, Carolina y sus amigos comieron 2 1/5 partes de torta.

Answer:

the total payment need to pay is $525

Step-by-step explanation:

Given that

The amount at promissory note issued is $500

The rate of interest is 10%

And, the time period is 180 days

So, the total payment included is

= $500 + ($500 × 10% × 180 days ÷ 360 days)

= $500 + $25

= $525

hence, the total payment need to pay is $525

Based on the given residual plot, it is essential to evaluate whether the linear model is a good fit for predicting the cost of a standard postage stamp.

A well-fitted linear model should display a random scatter of residuals, without any noticeable patterns or trends.

To determine if the model is a good fit, examine the residual plot for the following:

1. A random distribution of residuals around the horizontal axis (i.e., no discernible patterns or trends).

2. A constant spread of residuals throughout the entire range of predictor values (i.e., homoscedasticity). If these conditions are met in the residual plot, then the linear model is likely a good fit for the data. If not, a different model should be considered for better prediction accuracy.

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Answer:

x = 24

Step-by-step explanation:

you can match angle R with angle A to get the equation 3x-2 = 70

3x = 72

x = 24

(a) the required monthly loan payment on the car is approximately $528.23, (b)your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment, (c)it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

(a) The required monthly loan payment on the car can be calculated using the formula for the monthly payment on a loan. Given a car loan of $28,000, financed at an interest rate of 0.50% per month for 60 months, the monthly payment can be determined using the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Plugging in the values, we have:

Monthly Payment = (28000 * 0.005) / (1 - (1 + 0.005)^(-60))

Calculating this, the required monthly loan payment on the car is approximately $528.23.

(b) After making the 24th monthly payment, your friend still owes a remaining balance on the car loan. To calculate this, we need to determine the remaining balance based on the number of payments made and the original loan amount. We can use the formula:

Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Payments - (Monthly Payment * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate)

Plugging in the values, we have:

Remaining Balance = 28000 * (1 + 0.005)^24 - (528.23 * ((1 + 0.005)^24 - 1) / 0.005)

Calculating this, your friend still owes approximately $17,833.86 on the car loan after the 24th monthly payment.

(c) If your friend decides to pay $100 more each month after the 24th payment, we can calculate the number of months it will take her to pay off the remaining loan balance. Using the increased monthly payment, we can calculate the new remaining balance and divide it by the increased monthly payment to determine the number of months needed to pay off the loan.

New Remaining Balance = Remaining Balance - (Monthly Payment + Additional Monthly Payment) * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate

Number of Months = New Remaining Balance / (Monthly Payment + Additional Monthly Payment)

Plugging in the values, we have:

New Remaining Balance = 17,833.86 - (528.23 + 100) * ((1 + 0.005)^x - 1) / 0.005

Number of Months = New Remaining Balance / (528.23 + 100)

By solving the equation, it will take your friend approximately 23 months (rounded up to the nearest month) to pay off the remaining loan she owes after the 24th payment, given the increased monthly payment of $100.

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Answer:

A, C, and D

Step-by-step explanation:

Answer:

A)

C)

D)

Step-by-step explanation:

Let's go through each answer choice.

A) Since -3 is to the right of -4.5 on a number line, it is greater than -4.5

B) Since -32 is to the left of -4.5 on a number line, it is less than -4.5

C) Since 13 is to the right of -4.5 on a number line, it is greater than -4.5

D) Since 2.5 is to the right of -4.5 on a number line, it is greater than -4.5

E) Since -5.2 is to the left of -4.5 on a number line, it is less than -4.5

Therefore, the answer is A), C), and D).

To find the probability that a student break lasts more than 7 minutes, we can use the z-score formula to standardize the break time and then use the standard normal distribution table or a calculator to find the probability. The probability that a student break lasts more than 7 minutes is approximately 0.3745 or 37.45%.

Step 1: Calculate the z-score.
The z-score formula is given by:
z = (X - μ) / σ
where X is the break time, μ is the mean, and σ is the standard deviation. In this case, X = 7 minutes, μ = 6.3 minutes,

and σ = 2.2 minutes. Plugging in these values:
z = (7 - 6.3) / 2.2 ≈ 0.32
Step 2: Find the probability using the standard normal distribution table or a calculator.
Now that we have the z-score, we can find the probability that a student break lasts more than 7 minutes. We want to find the area to the right of the z-score (0.32) since we are interested in break times longer than 7 minutes.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = 0.32 is approximately 0.6255. However, we want the area to the right of z = 0.32, which is given by:
Area to the right of z = 1 - Area to the left of z
Area to the right of z ≈ 1 - 0.6255 ≈ 0.3745.

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Answer:

4.17

Step-by-step explanation:

6000x = 25000

x = 25000 / 6000

x = 4.17

1 mile is equal to 640 acres. Therefore, a lot that is 1/2 mile by 1/2 mile is approximately equal to 160 acres.

To determine the number of acres in a lot that is 1/2 mile by 1/2 mile, we need to convert the measurements to the same unit and then use the conversion factor for acres.

1 mile is equal to 640 acres. Therefore, we can calculate the area in square miles first.

Area = Length x Width = (1/2 mile) x (1/2 mile) = 1/4 square mile

To convert square miles to acres, we multiply by the conversion factor of 640 acres per square mile:

Area in acres = (1/4 square mile) x (640 acres/square mile) = 160 acres

Therefore, a lot that is 1/2 mile by 1/2 mile is approximately equal to 160 acres.

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Answer:

The answer is 9

Step-by-step explanation:

for the equation:

move the -6x

x^2 + c - 6x

To find c :

c = (b/2)^2

this means you have to divide the coefficient of x by 2 then square the result

If you dont understand I put a picture of all the steps

Answer: You earn more per pound recycling copper than aluminum.

Step-by-step explanation:

Based on the past data indicating that 30% of the general population holds the belief that life exists elsewhere within 4% of the real answer, we can use statistical analysis to determine the level of confidence we can have in this statement.

With a 95% confidence level, we can say that there is a high likelihood that this belief is true within a margin of error of 4%. In other words, we can be 95% confident that the true percentage of people who believe that life exists elsewhere within 4% of the real answer falls somewhere between 26% and 34%.

Based on the information provided, it seems that 30% of the general population believes that life exists elsewhere in the universe. There is a 95% confidence level that the true percentage of people holding this belief is within 4% of the given 30% estimate. This means that the actual percentage of people with this belief likely falls between 26% and 34%.

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Answer:

Step-by-step explanation:

Initial number is 5200

Every year the number increases by 5%

It can be represented as:

Correct choice is C

Answer:

D

Step-by-step explanation:

In this case, the marked price of 220 is the cost price and discount of 20% is announced on sales, so the selling price is 176.

The t-shirt costs $166.5 to purchase. To do this, multiply the listed price (220) by the discount rate (20%) stated as a decimal. This will give you the amount of the discount (0.20).

220*0.20 =44

The selling price is then determined by deducting the discount (44) from the marked price (220):

220-44 =176

Before applying any markups or reductions, the retailer paid the item's cost price, commonly referred to as the wholesale price. The price a consumer pays to purchase an item is known as the selling price. The selling price will be less than the advertised price if a discount is being offered, and the difference between the two represents the discount.

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