Simplify -10 + 5c - (-4) + (-1Oc)

Answer:

Step-by-step explanation:

The value should be reported as follows:

25.1 ± 0.1

In this case, the value has been rounded to the same decimal place as the uncertainty, which is the first decimal place. The uncertainty is rounded to one significant figure to reflect the precision of the measurement. The value is reported with one decimal place, which is the same as the uncertainty, to maintain consistency.

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Answer:

Step-by-step explanation:

simple! plug in the 5 for x, f(5)=2(5)+8

f(5)=10+8

f(5)=18

f(8)=3(8)+4

f(8)=28

The expression using brackets is (3x)(x⁴) + (2)(2) = 26

From the question, we have the following parametes that can be used in our computation:

7x5-4x5+16÷4=26

Express the superscripts in the expression properly

So, we have the following representation

7x⁵ - 4x⁵ + 16 ÷ 4 = 26

Evaluate the like terms

3x⁵ + 16 ÷ 4 = 26

Divide 16 by 4

3x⁵ + 4 = 26

Factorize and use brackets

(3x)(x⁴) + (2)(2) = 26

Hence, the expression is (3x)(x⁴) + (2)(2) = 26

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You surveyed 30 students to see how many CDs they owned.

The number of students who owned 5 - 8 CDs was:

= 15

The number of students who owned 9 - 12 CDs was:

= 10

The number of students who owned 13 - 16 CDs was:

= 5

The number of students who owned 17 - 20 CDs was:

= 0

The total number of students surveyed is the sum of the above:

= 15 + 10 + 5 + 0

= 30 students

30 students were surveyed for this study.

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The area of the rectangle is 55x² + 4x - 12. Option D

The formula for calculating the area of a rectangle is expressed as;

A = lw

Given  that the parameters are given as;

For rectangle 1;

Area = 5x(7x - 2)

expand the bracket

Area = 35x²- 10x

For rectangle 2:

Area = 15x - 6(6x + 2)

expand the bracket

Area = 90x² - 30x + 36x - 12

Area = 90x² + 6x - 12

subtract the values

Area = 90x² + 6x - 12 - (35x²- 10x)

Area = 55x² + 4x - 12

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Using trigonometric ratio, the value of cot β = 2√15/3

Using the knowledge of trigonometric ratio;

To find cot β, we can use the relationship between tan and cot.

cot β = 1 / tan β

Given that tan β = √15/10, we can substitute this value into the formula:

cot β = 1 / (√15/10)

To find cot value of this angle, we have to rationalize the surd.

cot β = 1 / (√15/10) * (√15/10)

Simplifying further:

cot β = 10 / √15

cot β = (10 / √15) * (√15 / √15)

cot β = 10√15 / 15

cot β = 2√15 / 3

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Answer:

Part A)  The length of the hypotenuse of triangle ABC is

Part B) The length of the shorter leg of triangle ABC is

Part C) The length of the longer leg of triangle ABC is

Step-by-step explanation:

see the attached figure  to better understand the problem

Step 1

Find the length of the longer leg of triangle ABC  (side BC)

we know that  

In the right triangle DBC  

substitute the values and solve for BC

Step 2

Find the length of the shorter leg of triangle ABC  (side AC)

we know that  

In the right triangle ACD

substitute the values and solve for AC

Step 3

Find the length of the hypotenuse of triangle ABC (side AB)

Applying the Pythagoras theorem

we have

substitutes

The solution is :

 15. the length of the hypotenuse of the triangle ABC,  AB = (40/3)√3

 16. The shorter leg of ΔABC is BC:  BC = (20/3)√3

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, we have,

The ratios of side lengths in the "special" 30-60-90° triangle are ...

 1 : √3 : 2

If D is the point where the altitude meets AB, then we have for the left triangle ...

 CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

 BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

 BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

15.

The hypotenuse of ΔABC is AB, shown above to be ...

 AB = 40/√3 = (40/3)√3

16.

The shorter leg of ΔABC is BC, shown above to be ...

 BC = 20/√3 = (20/3)√3

Hence, The solution is :

 15. the length of the hypotenuse of the triangle ABC,  AB = (40/3)√3

 16. The shorter leg of ΔABC is BC:  BC = (20/3)√3

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Step-by-step explanation:

x=120⁰

hdbdbdddfhcydhgdjvds

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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θ is in Quadrant I and tanθ = 5/12, the value of tan(4θ/5) to the nearest hundredth is approximately 18.10. The correct option is A.

To find the value of tan(4θ/5), we need to use trigonometric identities and the given information that θ is in Quadrant I and tanθ = 5/12.

Let's start by finding the value of θ. Since tanθ = 5/12, we can determine the corresponding angle using the inverse tangent function:

θ = tan⁻¹(5/12)

Using a calculator, we find that θ ≈ 22.62 degrees.

Next, we need to find 4θ/5. Plugging in the value of θ, we have:

4θ/5 = (4 * 22.62) / 5

4θ/5 ≈ 90.48 degrees

Now, we want to find tan(4θ/5). Since tan is a periodic function with a period of 180 degrees, we can subtract 180 from the angle if it is greater than 180 degrees. In this case, 90.48 degrees is less than 180 degrees, so we can proceed with finding tan(4θ/5) directly.

Using a calculator or trigonometric table, we find that tan(90.48 degrees) ≈ 18.10.

Therefore, the value of tan(4θ/5) to the nearest hundredth is approximately 18.10.

The correct answer is (A) 18.10.

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Answer: No, it’s not a statistical question

Step-by-step explanation:this question only pertains to one person and it not something that can be represented as a statistic.

Answer:

Subtract 11 both sides to isolate the variable and it's cooeficient.

Step-by-step explanation:

Given equation:

The main goal to determine the solution of the equation is to isolate the variable that is present in the equation.

(1) Subtract 11 both sides to isolate the variable and it's cooeficient.

(2) Simplify if possible.

(3) Divide the cooeficient (-3) both sides to remove the cooeficient from the variable.

Once the variable has been isolated, the opposite side of the variable will be the solution to the variable.

Step-1: Subtract 11 both sides

Step-2: Simplify (if possible)

Step-3: Divide the cooeficient of x (-3) both sides

Therefore, the first step in simplifying the expression (11 - 3x = 44) is to subtract 11 both sides to isolate the variable and it's cooeficient. When the expression is simplified, we get the solution x = -11.

Given:

Total number of students surveyed= 122

Studied in the cafeteria = 79

Studied in the student union = 56

Studied in both the student union and cafeteria = 24

To find:

Number of student those are did not study in either the cafeteria or the student union.

Solution:

Let A be the event that student studied in the cafeteria.

B be the event that student studied in the student union.

According to the question,

\(n(S)=122\), where S is sample space.

\(n(A)=79\)

\(n(B)=56\)

\(n(A\cap B)=24\)

Now,

\(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)

\(n(A\cup B)=79+56-24\)

\(n(A\cup B)=111\)

So, 111 students studied in either the student union or cafeteria.

\(n(A\cup B)=n(S)-n(A\cup B)\)

\(n((A\cup B)')=122-111\)

\(n((A\cup B)')=11\)

Therefore, 11 students not study in either the cafeteria or the student union.

When a nonlinear system of equations contains one linear function that touches the quadratic function at its maximum, then the system has one solution

A system of equations is considered nonlinear if it contains at least one nonlinear equation. One linear function in a nonlinear system of equations touches the quadratic function at maximum. It illustrates one solution.

The given system of equation is presented as follows;

Linear function: f(x) = mx + c

Quadratic function: f(x) = ax² + bx + c

It should be noted that given that the linear function touches the quadratic function at maximum we have;

ax² + bx + c = 0

Therefore, if a nonlinear system of equations contains one linear function that touches the quadratic function at its maximum has one solution.

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This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.

The discrepancy between the purchase price and the face value is the amount of the discount. A rebate is a specific kind of cost reduction or deduction for a product. An amount or percentage off the regular retail cost of an item or service is known as a rebate. You could be given the option to get, as an illustration, a $10 or 10% discount off the product's advertised price. a decrease in the overall quantity or value of something (see gross entry 1 for further information). Regular or routine price reductions. Give your clients a 10% discount.

This is an experimental research since the car wash owner will provide various discounts and then watch the extra money come in.

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Answer:

a)4/3

b)9/20 or 0.45

c)96

Step-by-step explanation:

a) j=3

72=20j+9p

72=20(3)+9p

72=60+9p

-9p=60-72

-9p=-12

p=-12/-9

p=4/3

b) m =1/2

20k-5=8m

20k-5=8(1/2)

20k-5=4

20k=4+5

20k=9

k=9/20 or 0.45

c) k=18

p+1/3k-20=82

p+1/3(18)-20=82

p+6-20=82

p=82+20-6

p=96

idk if this is right but I tried my best heh-

The amount of water that has entered the pool over these five minutes is 42.5 gallons.

Given the rate at which water enter the pool W(t). To calculate the amount of water that has entered the pool over these five minutes, we integrate W(t) over the interval t = 0 to t = 5.

\(Amount\ of \ water=\int\limits^0_5 {W(t)} \, dt \\\\\\Amount\ of \ water=\int\limits^0_5 {(1+3t)} \, dt \\\\\\Amount\ of \ water=[t+1.5t^2]_0^5\\\\\\Amount\ of \ water=42.5\ gallons\)

The amount of water that has entered the pool over these five minutes is 42.5 gallons.

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The number of cars that must be made to minimize the unit cost is 300 cars which is determined by differentiation.

Differentiation is a mathematical process that determines the instantaneous rate of change of a function based on one of its variables. The most common example is velocity, which is the rate of change of displacement with respect to time. Anti-differentiation is the inverse of finding a derivative.
Differentiation is used to calculate the rate of change of quantities in real time.

Since, we have been given the cost function to be function \((cx)= 1.1^{2} - 660x+107,357\) then we have to find the first differentiation in order to get the value and this will be:-

\((cx)= 1.1^{2} -660x+107,357\\2.2x=660\\x=\frac{660}{2.2} \\x=300\)

Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The response rate of the survey conducted by Megan to study bullying in high school is 0.4 or 40%

How to Calculate Response Rate?

The response rate can be calculated by dividing the number of completed survey responses by the number of people who viewed or started the survey.

To convert this to a percentage, multiple your final number by 100.

According to the giving question:

The number of completed survey responses = 400

The number of people who started the survey = 1,000

∴ Response rate = 400/1,000

                           = 0.4 or 40%

Hence the response rate is 0.4 or 40%.

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Answer:

\(135^\circ\)

Step-by-step explanation:

To convert radians to degrees, use the formula \(x^\circ=r\frac{180}{\pi}\) where \(r\) is the number of radians:

\(x^\circ=r\frac{180}{\pi}\)

\(x^\circ=(\frac{3\pi}{4})(\frac{180}{\pi})\)

\(x^\circ=\frac{540}{4}\)

\(x^\circ=135\)

Therefore, \(\frac{3\pi}{4}\) radians is \(135^\circ\)

Answer:

b=-5

Step-by-step explanation:

Divide by -9 to eliminate the -9 on -9b

(Since -9b is the same thing as -9 times b we can use the inverse of multiplication which is division to eliminate the -9 from b but we need to do it on both sides to make it balance)

-9b/-9=45/-9

b=-5

Answer:

The answer is x=11

Step-by-step explanation:

\( \frac{12}{8} = \frac{2x + 5}{x + 7} \\ 4x + 10 = 3x + 21 \\ x = 11\)

Hello,

\(0\leq a\leq 1 \Longrightarrow 0*a\leq a*a\leq 1*a \Longrightarrow 0 \leq a^2 \leq a\\\\0\leq a^2\leq a \Longrightarrow \sqrt{0} \leq \sqrt{a^2} \leq \sqrt{a} \\\\The\ function\ y=x^2\ is\ increasing\\\\Answer A\\\\ex: a=0.5 \\\\a^2=0.25\\\\\sqrt{a}=\dfrac{\sqrt{2}}{2}\approx{0.7071...}\\\\and\ 0.25\leq 0.5 \leq 0.7071...\)

1, 140 °

2, 40°

3, 100 °

4, 100°

5, 40°

6, 90 °

7, 120 °

8, 130 °

Step-by-step explanation:

1, BOA IS EQUAL TO FOH = 140°

2, FOE EQUAL TO BOA = BOA = 40° = FOE = 40°

3, BOA° + GOF° =40° + 60° = 100 °

4, GOE = BOC WHICH MEAN GOE = 100° = BOC = 100°

5, COD = HOG =40 °

6, EOD= AOG = 90°

7, AOD = GOE + COD = 100° + 40 ° = 140°

8, BOG = 140 °

The Distance between the given parallel planes is 8.84.

According to the statement

we have given that the two parallel planes and we have to find the distance between them.

So, For this purpose, we know that the

First let us find a point on one plane. For this in plane 9z +3x - 3y = 2

assume x = 0 and y = 0 then and hence (0,0,2/9) on this plane.

Now we find the distance between point (0,0,2/9) and plane 6z -2y + 2x =0

So,

As distance from a point to plane is

\(D= \frac{|ax_1+by_1+cz_1+d|}{\sqrt{ (a^2+b^2+c^2)}}\)

And

now substitute the values in then

\(D= \frac{|2*0+ (-2)0+6*2/9+0|}{\sqrt{ 36 +4+4)}}\)

Then the value becomes

\(D= \frac{4/3}{\sqrt{ (44)}}\)

\(D= \frac{4\sqrt{44} }{3}\)

Then solve it

\(D= \frac{26.52}{3}\)

then

D = 8.84

So, The Distance between the given parallel planes is 8.84.

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the proportionality constant is 20 and in 8 ours it will cover 160 miles.

What is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

The slope of he given graph will be (30-10)/(2-1) = 20

So here the proportionality constant is 20.

we can write y = 20x

This means in 8 ours it will cover 8*20 = 160 miles.

Hence, the proportionality constant is 20 and in 8 ours it will cover 160 miles.

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