Measure Progress Check Question 10
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A woman puts £3,500 into a bank account. The interest rate is 5% per year.
How much will be in the account after 1 year?

Answer:

Step-by-step explanation:

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer: $8,849

Step-by-step explanation: 17,698 divided by two people is 8,849, therefore each sister paid $8,849.

Answer: $8849

Step-by-step explanation: We are given that the total amount both sisters pay is $17698. They each pay for a fraction though. That fraction is 1/2 since they each pay for half. We multiply this fraction by the total which is 17698 to find our answer.

If there were three sisters and they each paid one-third, we would multiply the total price by 1/3 to find our answer.

Answer:

Step-by-step explanation:

To find Bianca's walking speed, we need to divide the distance she walks by the time it takes her to walk that distance. We can do this by converting both the distance and time to the same unit of measure.

Since 1 hour is equal to 60 minutes, 1/3 of an hour is equal to 1/3 * 60 minutes = 20 minutes. Now that we have the distance in miles and the time in minutes, we can divide the distance by the time to find Bianca's walking speed.

5/6 of a mile is equal to 5/6 * 1 mile = 0.83 miles. So, Bianca's walking speed is 0.83 miles / 20 minutes = 0.0415 miles per minute. To convert this to miles per hour, we can multiply by the conversion factor of 60 minutes per hour. This gives us a walking speed of 0.0415 miles/minute * 60 minutes/hour = 2.49 miles per hour. So, Bianca's walking speed is 2.49 miles per hour.

Answer:

y = 2x + 10

Step-by-step explanation:

Hi there!

We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope (m) of the line

The slope can be calculated from 2 points using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes

\(x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2\)

Substitute these values into the formula (note: remember that the formula has subtraction in it!)

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2--4}{-6--7}\)

Simplify

m=\(\frac{-2+4}{-6+7}\)

Add the numbers

m=\(\frac{2}{1}\)

Divide

m=2

The slope of the line is 2

We can substitute that in:

y = 2x + b

Now we need to find b

As the equation passes through both  (-7,-4) and (-6,-2), we can use either point to help solve for b

Taking (-6, -2) for example:

Substitute -6 as x and -2 as y into the equation.

-2 = 2(-6) + b

Multiply

-2 = -12 + b

Add 12 to both sides

-2 = -12 + b

+12  +12

___________

10 = b

Substitute 10 as b.

y = 2x + 10

Hope this helps!

Topic: Finding the equation of a line

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top I think he or she is right

The length of the AB in the given right triangle is √3/6

Given that, a right triangle with the base measure 6 units and an acute angle 30°,

We need to find the measure of side AB,

So, we will use the concept of trigonometric ratios,

Tan 30° = AB / AC

Tan 30° = AB / 6

1 / √3 = AB / 6

AB = √3/6

Hence the length of the AB in the given right triangle is √3/6

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Answer and Step-by-step explanation:

The equation would be y = 60h

Divide 180 by 3, and you get 60. This is the amount of miles that can be driven in an hour.

#teamtrees #PAW (Plant And Water)

X = 1 4 5 6

Y = 20 8 4 0

From the function: Y = 24 - 4X

If X = 1, then Y = 24 - 4(1) = 20

If X = 4, then Y = 24 - 4(4) = 8

If X = 5, then Y = 24 - 4(5) = 4

If X = 6, then Y = 24 - 4(6) = 0

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"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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Answer:

housing , savings and food

housing , food and transport

Answer:

food , transportation , and clothing

Step-by-step explanation:

Answer:

2.05 secs

Step-by-step explanation:

we will use quadratic formula to work out the time t.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

where a is the value of the first coefficient, b is value of the second and c is value of the constant.

h = -9t² + 15t + 7

we need water level, so h = 0.

-9t² + 15t  + 7 = 0

a = -9, b = 15, c = 7.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

= ((-(15) ± √((15)² - 4(-9)(7))) ÷ 2(-9))

= ((-15 ± √(225 - -252)) ÷ -18)

= ((-15 ± √(225 + 252)) ÷ -18)

= ((-15 ± √(477)) ÷ -18)

= -0.380 or 2.05

t is time, so it has to be positive.

t = 2.05 seconds to nearest one hundredth

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

The correct information about the function is that B. the slope of Function G is less than the slope of Function F.

It should be noted that the slope is the process of finding the rate of change of the value y which is the dependent variable of the function changes with respect to that of the variable x that is the independent variable.

Here, the slope itself describes the direction and steepness of the line. The slope of Function G is 2, which is less than the slope of 3 that Function F has.

Therefore, the slope of Function G is less than the slope of Function F.

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We need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 Percent confidence is 170.

To find the sample size to estimate the mean with an error of +4 and 95 percent confidence, we need to use the formula:

n = [(z*sigma)/E]^2

Where:
n = sample size
z = z-score for 95% confidence level (which is 1.96)
sigma = standard deviation (unknown in this case)
E = maximum allowable error (which is +4 in this case)

We are given that o=12, which is the population standard deviation. Since we do not have any information about the sample standard deviation, we can use the population standard deviation as an estimate. Therefore, we can substitute o=12 in the above formula to get:

n = [(1.96*12)/4]^2
n = 169.64

Since we need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 percent confidence is 170.

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Answer:

3

2

Step-by-step explanation:

Answer:

$50

Step-by-step explanation:

40x1.25=50

price with discount X Discount price to undo it= Original price

Answer:

2. y = mx + b

Explanation:

The slope intercept form of linear equation can be written in the form;

Where;

m = slope

b = intercept (on the y axis)

Therefore, for the given question, the equation that represents the slope-intercept form of linear equation is;

2. y = mx + b

Answer:

p = 18

Explanation:

\(\hookrightarrow \sf 4(p - 7) = 44\)

\(\sf change \ sides\)

\(\hookrightarrow \sf p-7\right}=\frac{44}{4}\)

\(\sf simplify\)

\(\hookrightarrow \sf p-7\right}= 11\)

\(\sf change \ sides\)

\(\hookrightarrow \sf p\right}= 11+7\)

\(\sf final \ answer\)

\(\hookrightarrow \sf p\right}= 18\)

Answer:

\(4( p - 7)=44\)

Divide both sides by 4:

\(\implies \dfrac{4(p - 7)}{4}=\dfrac{44}{4}\)

Simplify:

\(\implies p - 7=11\)

Add 7 to both sides:

\(\implies p - 7+7=11+7\)

Simplify:

\(\implies p=18\)

Answer:

π/6 and 5π/6

Step-by-step explanation:

Graphing the equation or using a unit circle, we can find these values out pretty easily

Answer:

translation

Step-by-step explanation:

Answer:

I think it's dilation or none

Step-by-step explanation:

First we will obtain the lateral surface area

we have

h=11m

r=7m

we substitute the values

For the total surface area we will use the next formula

we substitute the values

The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

<95141404393>

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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