A rectangular swimming pool is 21 metres
wide and 50 metres long. Calculate the length
of the diagonal to 1 decimal place.​

For this case we must simplify the following expression:

[tex]8- \frac {4} {5} x-14-2x =[/tex]

We add similar terms:

[tex]8-14- \frac {4} {5} x-2x =[/tex]

We take into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

[tex]-6+ (\frac {-4-10} {5} x) =\\-6+ (\frac {-14} {5} x) =\\-6- \frac {14} {5} x[/tex]

Finally, the simplified expression is:

[tex]-6- \frac {14} {5} x[/tex]

ANswer:

[tex]-6- \frac {14} {5} x[/tex]

Answer:

32

Step-by-step explanation:

4 x 8 = 32

Answer:

32 quarters

Step-by-step explanation:

if there are 4 stack with 8 quarters in each stack, then we know that all we have to do is multiply 4 x 8 which equals 32

The value of b is: 4

Step-by-step explanation:

The given polygon is a convex polygon with three sides. A polygon with three sides is called triangle. The sum of interior angles of a triangle is 180°

So,

[tex]Sum\ of\ Angles = 180\\(b+41)+(101)+(b+30) = 180\\b+41+101+b+30 = 180\\2b+172 = 180\\2b = 180-172\\2b = 8[/tex]

Dividing both sides by 2

[tex]\frac{2b}{2} = \frac{8}{2}\\b = 4[/tex]

Hence,

The value of b is: 4

Keywords: Polygons, Triangles

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The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

a) The rate of change is $475 per month

b) The initial value is $125

c) The independent variable is the number of months (x)

d) The dependent variable is the total cost after each month (y)

Step-by-step explanation:

The given is:

Assume that the total cost is y for x months

∵ The registration fee = $125 ⇒ paid once

∵  The parents pay $475 per month for  tuition

∵ The number of months is x

∴ The total cost y = 475 x + 125

The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

∵ y = 475 x + 125 is in the form of the linear equation y = m x + b,

  m is the slope of the line and b is the y-intercept

∵ The slope of the line m is the rate of change y with respect to x

∴ m = 475

∴ The rate of change is $475 per month

a) The rate of change is $475 per month

∵ b is the initial value of y at x = 0

∴ b = 125

∴ The initial value is $125

b) The initial value is $125

∵ The independent variable is x

∴ The independent variable is the number of months (x)

c) The independent variable is the number of months (x)

∵ The dependent variable is y

∴ The dependent variable is the total cost after each month (y)

d) The dependent variable is the total cost after each month (y)

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Answer:

x > - 2

Step-by-step explanation:

Given

7 + x > 5 ( subtract 7 from both sides )

x > - 2

Answer:

[tex]\frac{32xy}{3}[/tex]

Step-by-step explanation:

Answer:

cot(∅) = [tex]\frac{10\sqrt{15} }{15}[/tex]

Step-by-step explanation:

tan ∅ and cot ∅ are inverse functions

therefore the inverse of

tan ∅ = √15 / 10

is equal to

cot ∅ = 10 / √15

Rationalizing the denominator

[tex]\frac{10}{\sqrt{15} }[/tex] * [tex]\frac{\sqrt{15} }{\sqrt{15} }[/tex]

cot ∅ = [tex]\frac{10\sqrt{15} }{15}[/tex]

Answer:(2\sqrt(15))/(3)

Step-by-step explanation:

There are 60 miles in Jadon's trip.

Step-by-step explanation:

Distance covered by Jadon = 42 miles

This is 70% of his entire trip.

Let,

x be the total number of miles in Jadon's trip.

We know that,

70% of x = 42 miles

[tex]\frac{70}{100}*x=42\\0.7x=42[/tex]

Dividing both sides by 0.07;

[tex]\frac{0.7x}{0.7}=\frac{42}{0.7}\\x=60\ miles[/tex]

There are 60 miles in Jadon's trip.

Keywords: distance, percentage

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Answer:

The given description is equivalent to the algebraic expression,

[tex](\frac {11}{k})^{2}[/tex]

Step-by-step explanation:

The given description is ,

'The square of the ratio of 11 and k'

which is equivalent to the algebraic expression,

[tex](\frac {11}{k})^{2}[/tex]

Answer:

The total loss percentage is 6.25%.

Step-by-step explanation:

Let the cost price of the first cycle is $x.

So, for the first cycle, 25% profit is there for selling the cycle at $2500.

Then, [tex]x(1 + \frac{25}{100}) = 2500[/tex]

⇒ 1.25x = 2500

⇒ x = $2000

Again, let us assume that the cost price of the second cycle is $y.

So, by selling the cycle at $2500 there is a loss of 25%.

Therefore, [tex]y(1 - \frac{25}{100} ) = 0.75y = 2500[/tex]

⇒ y = $3333.33

Therefore, the total cost price of two cycles = $(2000 + 3333.33) = $5333.33 and total selling price is $(2500 + 2500) = $5000.

Therefore, the total loss percentage is [tex]\frac{5333.33 - 5000}{5333.33} \times 100 = 6.25[/tex] % (Answer)

Answer:

The correct option is 4) 0.72.

Step-by-step explanation:

Consider the provided information.

Let us consider that there are 100 members.

(Note: you can take any number the answer will remain the same.)

90% of its members drank protein shakes and of the members who drank  protein shakes.

90% of 100 is 90.

Thus, 90 members drank protein shake.

Of the members who drank   protein shakes, 30% took weight-loss medication.

30% of 90 is 27.

That means 27 out of 90 took weight loss medication.

Out of 100 members 90 drank protein shakes that means 10 members does not take protein shakes.

Only 10% of members  who did not drink protein shakes took weight-loss medication.

10% of 10 is 1, that means 1 member out of 10 took weight loss medication.

Thus the required table is:

                                        Medication   Not Medication      Total

Drank shakes                       27                   63                      90

Doesn't Drank shakes          1                      9                        10

Total                                      28                   72                     100

Now we need to find the probability that a gym member does not take weight-loss medication.

72 out of 100 members does not take weight-loss medication.

Therefore, the required probability is: [tex]\frac{72}{100}=0.72[/tex]

Hence, the correct option is 4) 0.72.

Answer:

Step-by-step explanation:

1

2+2=4 because you add it ok well bye :)

Answer:

24% could be going to school by walking

Step-by-step explanation:

By adding the given percentages of students traveling by car, bus, and bike, and subtracting from 100%, we find that 24% of students use other methods to travel to school.

To find the other method of traveling to school not mentioned among car, bus, and bicycle, we first need to add up the provided percentages for these modes of transportation: 20% (car) + 48% (bus) + 8% (bike) = 76%. Since all the percentages must add up to 100%, we subtract the sum of these percentages from 100% to determine the remaining percentage. Therefore, 100% - 76% = 24%. So, 24% of students travel to school by other methods that are not specified (walking, skateboarding, etc.).

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Answer:

c

Step-by-step explanation:

Answer:

-1.28

Step-by-step explanation:

1=ln(x+4)

ln(x+4)=1

e^ln(x+4)=e^1

x+4=e

x=e-4=-1.28

Answer:

The cost of the 20 fruit cup is $ 60  .

Step-by-step explanation:

Given as :

The total students for fruit cup party = 18

The total teachers for fruit cup party = 2

The cost of each fruit cup =$ 3

The delivery charge = $ 10

So, The total number of people for party = Total number of student + Total number of teachers

Or , The total number of people for party = 18 + 2 = 20

∵ each fruit cup cost $ 3

∴ The cost of 20 fruit cup = $ 3 × 20

I.e The cost of 20 fruit cup = $ 60

Hence The cost of the 20 fruit cup is $ 60  . Answer

The range of the function for the fruit-cup party is $10 to $70, including the delivery charge and the cost of the fruit cups.

To find the range of the function for the fruit-cup party, we need to consider the total cost of the fruit cups and the delivery charge. The delivery charge is a fixed cost of $10. The cost of each fruit cup is $3. So, the total cost of the fruit cups for the 18 students and 2 teachers is (18 + 2) × $3 = $60. Therefore, the range of the function is $10 to $70, which includes the delivery charge and the total cost of the fruit cups.

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Answer:

We conclude that the calibration point is set too high.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  1000 grams

Sample mean, [tex]\bar{x}[/tex] =  1001.1 grams

Sample size, n = 50

Alpha, α = 0.05

Population standard deviation, σ = 2.8 grams

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}[/tex]

We use One-tailed(right) z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778[/tex]

Now, [tex]z_{critical} \text{ at 0.01 level of significance } = 2.326[/tex]

Since,  

[tex]z_{stat} > z_{critical}[/tex]

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.

Final answer:

The null hypothesis is that the calibration point is set correctly and the alternate hypothesis is that the calibration point is set too high.

Explanation:

The appropriate null and alternate hypotheses for this hypothesis test are:

H0: The calibration point is set correctly (mean scale reading = 1000 grams)

H1: The calibration point is set too high (mean scale reading > 1000 grams)

This hypothesis test is a right-tailed test because the alternate hypothesis is testing for a value greater than the null hypothesis.

Answer: 55/7π

Step-by-step explanation:

circumference = 2πr

2πr = 55/7

r = 55/14π

d = 2r

d = 55/7π

Answer:

$15

Step-by-step explanation:

120/8=15

Answer:

Step-by-step explanation:

Total Cost of 8 copies of same CD =$120

Because the copies of the CD is same, the cost of each one should be same

Cost of one CD should be $120/8=$15

Answer:

Step-by-step explanation:

1d

2a

3b

4c

The distributive property states that performing an operation on a sum or difference (either multiplication or division) is equivalent to performing that operation on each addend separately and then summing or subtracting the results. As an example, the statement 2*(3 + 4) can be rewritten as (2*3) + (2*4) to demonstrate the application of the distributive property.

The distributive property in mathematics states that the multiplication of a number by a sum is equivalent to the sum after each addend has been multiplied by that number individually. For example, if we had the expression 2*(3 + 4), using the distributive property, we could rewrite it as (2*3) + (2*4) which is 6 + 8, and both expressions equal to 14 (because 2*(3 + 4)=2*7=14).

So to match equivalent expressions using the distributive property, you would have to identify expressions that follow this rule. For example:

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Answer:

b. y=10x

Step-by-step explanation:

                                                             1

                                                            1.5

                                                             2

                                                            2.5

y represents distance (miles): 5

                                                 10

                                                 15

                                                 20

                                                 25

let the 2 points be:  (1,10) and (2,20) [from the given information]

then the equation of it can be given as :

[tex]y-B=(\frac{D-B}{C-A} )*(x-A)[/tex]

[tex]y-10=(\frac{20-10}{2-1} )*(x-1)\\[/tex]

this is also equal to, [tex]y-10=10*(x-1)\\y-10=10x-10\\y     =10x-10+10\\y=10x[/tex]

Answer:

The answer to your question is A.35

The perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2).

Since M, R, and T are midpoints of the sides of ABC, they divide each side into two equal parts. Therefore, AM = MB, BR = RC, and CT = TA.

Now, let's find the lengths of AM, BR, and CT.

1. **Length of AM:**

[tex]\[ AM = \frac{1}{2} \cdot AB = \frac{1}{2} \cdot 18 = 9 \][/tex]

2. **Length of BR:**

 [tex]\[ BR = \frac{1}{2} \cdot BC = \frac{1}{2} \cdot 10 = 5 \][/tex]

3. **Length of CT:**

[tex]\[ CT = \frac{1}{2} \cdot AC = \frac{1}{2} \cdot 14 = 7 \][/tex]

Now, we need to find the perimeter of quadrilateral ACRM:

[tex]\[ \text{Perimeter} = AM + BR + RC + CT \][/tex]

[tex]\[ \text{Perimeter} = 9 + 5 + 7 + 9 = 30 \][/tex]

So, the perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2). Please double-check the answer choices, as the calculated perimeter is not exactly matching any of the provided options.

The expression -y + 9z - 16y - 25z + 4 simplifies to -17y - 16z + 4 by combining like terms, which are the y terms and the z terms separately.

The task is to simplify the expression -y + 9z - 16y - 25z + 4. To do this, we will combine like terms.

First, combine the terms that contain y:

-y - 16y = -17y

Then, combine the terms that contain z:

9z - 25z = -16z

The number without a variable, which is 4 in this case, remains the same since it does not have any like terms to combine with.

Now, we put the simplified terms together:

-17y - 16z + 4

The expression is now simplified to its least terms.

Answer:

(24x)(19x2) 12/2 19

Step-by-step explanation:

(24x)(19x2) 12/2 19

Answer:

12.7 ft

Step-by-step explanation:

You're going to need to use acos

so

12 = acos (19) = 12.69

Then round up to 12.7

Answer:

Yes

Step-by-step explanation:

It is a Pythagorean Triple. A Pythagorean Triple is the sides of a triangle that fit perfectly into the Pythagorean Theorem, which is:

a²+b²=c²

12, 13, and 15 are numbers that you should know off the top of your head so if you see a triangle with 2 of those numbers, you instantly know the 3rd number.

~Stay golden~ :)

Answer: Yes

Step-by-step explanation: To determine if these side lengths can form a triangle, I attached a rule in the image provided which is very helpful to look at especially when you're new at this.

If a triangle has sides with lengths of 12, 15, and 13, notice that 12 + 15 or 27 is greater than 13.

So the sum of the lengths of two sides of the triangle is greater than the length of the third side.

This means that the triangle with sides of lengths of 12, 15, and 13, is possible.

Answer:

[tex]f(x)=0.5(0.2)^x[/tex]

Step-by-step explanation:

Exponential function can be in this form : [tex]f(x)=ab^x[/tex]

To find a and b we can use any two pairs from the table.

We can use (0, 0.5) and (1,0.1)

[tex]0.5=a*b^0\\a=0.5[/tex]

let's find b

[tex]0.1=0.5b^1\\b=0.2[/tex]

The exponential function represented by the table is [tex]\( f(x) = 3.125 \times (0.5)^x \)[/tex], where x can take values -2, -1, 0, 1, or 2, and f(x) corresponds to the values given in the table.

1. Examine the given table with two columns: x and f(x), where x takes values -2, -1, 0, 1, and 2, and f(x) takes corresponding values 12.5, 2.5, 0.5, 0.1, and 0.02.

2. Notice that as x increases by 1, f(x) decreases by a factor of 5 (12.5 / 2.5 = 5, 2.5 / 0.5 = 5, etc.), indicating an exponential decay pattern.

3. Write the general form of an exponential decay function:

 [tex]\[ f(x) = a \times b^x \][/tex]

  where a is the initial value and b is the decay factor.

4. Use the first row of the table (x = -2, f(x) = 12.5) to find the initial value, a:

  [tex]\[ 12.5 = a \times (0.5)^{-2} \] \[ 12.5 = a \times 4 \] \[ a = \frac{12.5}{4} = 3.125 \][/tex]

5. Substitute the initial value, a, into the exponential function:

  [tex]\[ f(x) = 3.125 \times (0.5)^x \][/tex]

Therefore, the exponential function represented by the table is [tex]\( f(x) = 3.125 \times (0.5)^x \)[/tex], where x can take values -2, -1, 0, 1, or 2, and f(x) corresponds to the values given in the table.

Answer:

See explanation

Step-by-step explanation:

        Statements                         Reasons

1. [tex]\overline{AD}\parallel \overline{BC}[/tex]                                        Given

2. [tex]\angle ADB\cong \angle CBD[/tex]      As alternate interior angles when parallel lines AD and BC intersect by ltransversal BD

3. [tex]\overline{AD}\cong \overline{BC}[/tex]                                     Given

4. [tex]\overline{BD}\cong \overline{DB}[/tex]                     Reflexive property

5. [tex]\triangle ADB\cong \triangle CBD[/tex]                  SAS postulate

6.  [tex]\angle ABD\cong \angle CDB[/tex]              Corresponding parts of congruent triangles are congruent

7. [tex]\overline{AB}\parallel \overline{CD}[/tex]            Inverse alternate interior angles theorem

Answer:

Part i) -14

Part ii) 11

Part iii) 4

Step-by-step explanation:

we know that

The average rate of change or slope using the difference quotient formula is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Part i) x= -3 and x= -1

In this problem we have

[tex]a=--3[/tex]

[tex]b=-1[/tex]

[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]  

[tex]f(b)=f(-1)=3(-1)^{2} -2(-1)+5=10[/tex]

Substitute

[tex]\frac{10-38}{-1+3}[/tex]

[tex]\frac{-28}{2}[/tex]

[tex]-14[/tex]

Part ii) x= -3 and x= 0

In this problem we have

[tex]a=--3[/tex]

[tex]b=0[/tex]

[tex]f(a)=f(-3)=3(-3)^{2} -2(-3)+5=38[/tex]  

[tex]f(b)=f(0)=3(0)^{2} -2(0)+5=5[/tex]

Substitute

[tex]\frac{5-38}{0+3}[/tex]

[tex]\frac{-33}{3}[/tex]

[tex]-11[/tex]

Part iii) x= (1-h) and x=(1+h)

In this problem we have

[tex]a=-(1-h)[/tex]

[tex]b=(1+h)[/tex]

[tex]f(a)=f(1-h)=3(1-h)^{2} -2(1-h)+5=3(1-2h+h^2)-2+2h+5=3-6h+3h^2+2h+3=3h^2-4h+6[/tex]  

[tex]f(b)=f(1+h)=3(1+h)^{2} -2(1+h)+5=3(1+2h+h^2)-2-2h+5=3+6h+3h^2-2h+3=3h^2+4h+6[/tex]  

Substitute

[tex]\frac{(3h^2+4h+6)-(3h^2-4h+6)}{1+h-(1-h)}[/tex]

[tex]\frac{8h}{2h}[/tex]

[tex]4[/tex]

Final answer:

To find the most number of miles you can drive on one tank of gas, divide the total miles driven by the total gallons used to calculate the miles per gallon (MPG). Then, multiply the MPG by the number of gallons in the gas tank to find the maximum number of miles that can be driven on one tank.

Explanation:

To find the most number of miles you can drive on one tank of gas, you can use the given information. You know that you just drove your car 450 miles and used 50 gallons of gas. Therefore, to find the miles per gallon (MPG), divide the total miles driven by the total gallons used. In this case, 450 miles divided by 50 gallons gives you an MPG of 9. This means that for every gallon of gas, your car can travel 9 miles.

Now, you know that the gas tank on your car holds 15 1/2 (or 15.5) gallons of gas. To find the maximum number of miles you can drive on one tank of gas, multiply the MPG by the number of gallons in the tank. So, 9 MPG multiplied by 15.5 gallons equals 139.5 miles. Therefore, the most number of miles you can drive on one tank of gas is 139.5 miles.

The most number of miles you can drive on one tank of gas is 139.5 miles.

To determine the most number of miles you can drive on one tank of gas, follow these steps:

Calculate the car's average miles per gallon (mpg):

You drove 450 miles using 50 gallons of gas.

The average mpg is calculated by dividing the total miles driven by the total gallons of gas used: [tex]\frac{450 \text{ miles}}{50 \text{ gallons}} = 9 \text{ mpg}.[/tex]

Determine the capacity of one full tank of gas in your car:

The gas tank holds 15 1/2 gallons of gas. Convert 15 1/2 to a decimal: [tex]15 \frac{1}{2} = 15.5 \text{ gallons}.[/tex]

Calculate the most number of miles you can drive on one full tank of gas:

Multiply the car's average mpg by the gas tank's capacity: [tex]9 \text{ mpg} \times 15.5 \text{ gallons} = 139.5 \text{ miles}.[/tex]

Answer:

A.10000

B.25 more trees must be planted

Step-by-step explanation:

⇒Given:

A.

⇒If the total trees per acre is doubled , which means :

total number of trees per acre [tex]t_{f}[/tex] = [tex]2*t_{i}[/tex] = 200

the yield will decrease by : [tex]t_{f}[/tex] - [tex]y_{i}[/tex]

[tex]y_{f}= 150-100= 50[/tex]

⇒total yield = [tex]50*200=10000[/tex]

B.

⇒to maximize the yield ,

let's take the number of trees per acre to be 100+y ;

and thus the average yield per acre = 150 - y;

total yield = [tex](100+y)*(150-y)\\=15000+50y-y^{2} \\[/tex]

this is a quadratic equation. this can be rewritten as ,

     ⇒   [tex]=15000+50y-y^{2}\\=15000+625 - (625 - 50y +y^{2})\\=15625 - (y-25)^{2}[/tex]

In this equation , the total yield becomes maximum when y=25;

⇒Thus the total number of trees per acre = 100+25 =125;