Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?

Answers

Answer 1

Answer:

The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 500[/tex]

     The standard deviation is  [tex]\sigma = 100[/tex]

The  percent of people who write this exam obtain scores between 350 and 650    

    [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]

Generally  

               [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

   [tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]

   [tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]

   [tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]

From the z-table  [tex]P(Z < -1.5 ) = 0.066807[/tex]

   and [tex]P(Z < 1.5 ) = 0.93319[/tex]

=>    [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]

=>  [tex]P(350 < X 650 ) = 0.866[/tex]

Therefore the percentage is  [tex]P(350 < X 650 ) = 86.6\%[/tex]


Related Questions

what must be added to 2/3 of 5.25 to make it 7.00​

Answers

(2/3)(5.25) + x = 7
3.5 + x = 7
x = 3.5

Answer:

3.5

Step-by-step explanation:

Well you have to find first 2/3 of 5.25. This means multiplication, which is 3.5. so to find how much to add to this to get 7, we have to subtract 3.5 from 7. 7-3.5=3.5. so we must add 3.5 to get 7. Hope this helps :D

Use the order of operations to simplify this expression 1.2x3.5x4.1= What

Answers

[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level

Answers

Answer:

their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster

The upper-left coordinates on a rectangle are (-1,4), and the upper-right coordinates are (3,4). The rectangle
has a perimeter of 24 units.
Draw the rectangle on the coordinate plane below.

Answers

Answer:

Step-by-step explanation:

Note that the perimeter of a rectangle P = 2(Length + Breadth)

The distance between the upper-left coordinates on a rectangle and the upper-right coordinates is the breadth of the rectangle. To get the breadth of the rectangle, we will use tgw formula for calculating the distance between two points as shown.

D = √(y2-y1)²+(x2-x1)²

Given the coordinates (-1,4) and (3,4), the distance between the coordinates where x1 = -1, y1 = 4, x2 = 3 and y2 = 4 will be expressed as.

B = √(4-4)²+(3-(-1))²

B = √0+4²

B = √16

B = 4

Hence the breadth of the rectangle is 4 units.

Substituting the breadth into the formula for calculating the perimeter will give;

P = 2(L+B)

24 = 2(L+4)

L+4 = 24/2

L+4 =12

L = 12-4

L = 8

Hence the length of the rectangle is 8 units.

The diagram of the rectangle on a coordinate is as given in the attachment below.

9. Find the mean of the following data :
Х
8
10
12
20
16
F
2
3
7
2
5​

Answers

Answer:

[tex] \boxed{13.15}[/tex]

Step-by-step explanation:

( See the attached picture )

Now,

Mean = [tex] \mathsf{\frac{Σfx}{n} }[/tex]

[tex] \mathsf{ = \frac{250}{19} }[/tex]

[tex] \mathsf{ = 13.15}[/tex]

------------------------------------------------------------------------

In the case of repeated data , follow the steps given below to calculate the mean :

Draw a table with 3 columnsWrite down the items ( x ) in ascending or descending order in the first column and the corresponding frequencies in the second column.Find the product of each item and it's frequency ( fx ) and write in the third column.Find the total of f column and fx column.Divide the sum of fx by the sum of f ( total number of items ) , the quotient is the required mean.

Hope I helped!

Best regards!

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)

Answers

This sequence converges to 0.

Proof: Recall that

[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]

is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].

Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then

[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]

[tex]\implies\dfrac1n<\varepsilon^2[/tex]

[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]

as required.

[tex]f(x) = {x}^{2} + 4x - 5[/tex] ; >-2
Find [tex] \frac{d {f}^{ - 1} }{dx} [/tex] at x=16​

Please show solving

Answers

The inverse function theorem says

[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}[/tex]

We have

[tex]f(x)=x^2+4x-5[/tex]

defined on [tex]x>-2[/tex], for which we get

[tex]f^{-1}(x)=-2+\sqrt{x+9}[/tex]

and

[tex]f^{-1}(16)=-2+\sqrt{16+9}=3[/tex]

The derivative of [tex]f(x)[/tex] is

[tex]f'(x)=2x+4[/tex]

So we end up with

[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}[/tex]

3

2

Vx

1

1

2 3 4 5 6 7 8 9 10 11 12 X

Magnets

Using equivalent ratios, which statements are true about the cost per magnet? Check all that apply.

The cost of 2 magnets is $1.

The cost of 9 magnets is $3.

The cost of 10 magnets is $3.

The cost of 4 magnets is $2.

The cost of 6 magnets is $2.

The cost of 3 magnets is $1.

Next

Submit

Save and Exit

Mark this and retum

Answers

Answer:

The cost of 3 magnets is $1

The cost of 9 magnets is $3

The cost of 6 magnets is $2

Step-by-step explanation:

The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost  $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.

A cubical sandbox has a volume of 91.125 cubic inches. What is the side length of the
sandbox?

Answers

Hey there! I'm happy to help!

To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.

We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.

∛91.125=4.5

Therefore, the side length of the sandbox is 4.5 inches.

I hope that this helps! Have a wonderful day! :D

If your starting salary is $40000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn one the first 16 years that you work

Answers

Answer:

Total amount in dollars= $64614.00

Step-by-step explanation:

Initial starting salary is $40000.

Rate of increase is 3%

Number of years is 16 years

The salary is compounded yearly.

Amount A after 16 years is given as

A= p (1+r/n)^ (nt)

A=40000(1+0.03/16)^(16*16)

A= 40000(1.001875)^(256)

A=40000(1.61534824)

A= 64613.92959

Total amount in dollars= $64614.00

Answer: the answer is $806275

Step-by-step explanation:

A p e x

which function represents the area of the triangle h(x)=1/2f(x)g(x)

Answers

Answer:

h=1/2fg

Step-by-step explanation:

Solve for x, h=1/2fg

It is true for all x; h=1/2fg

h=1/2fg

Both sides are equal

It is true for all x; h=1/2fg

(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems? (3 Marks) ii. Is a heavy drinker (2 Marks) iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem? (2 Marks) iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker? (2 Marks) v. If a person is found to be a non –drinker, what is the probability that this person has liver problems. (2 Marks)

Answers

Answer:

i. Has a liver problems?

= 0.08

ii. Is a heavy drinker ?

= 0.066

iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?

= 0.303

iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?

= 0.25

v. If a person is found to be a non –drinker, what is the probability that this person has liver problems?

= 0.104

Step-by-step explanation:

We have 2 Events in this question

Event A: People with liver problems

Event B : People without liver problems

Event A: People with liver problems

Let us represent people with liver problems as = (L)

a)8% have liver problems. = P(L)

Under liver problems we have:

b) 25% are heavy drinkers = P( L & H)

c) 35% are social drinkers = P( L & S)

d) 40% are non-drinkers. = P( L & N)

Event B( no liver problem)

Let us represent no liver problem as NL

We are not given in the question but Probability of having no liver problem = 100 - Probability of having liver problem

= 100 - 8% = 92 %

P(NL ) = 92%

From the question, For people without liver problems, we have:

a) 5% are heavy drinkers = P(NL & H)

b) 65% are social drinkers = P( NL & S)

c) 30% do not drink at all = P( NL & N)

An adult is chosen at random, what is the probability that this person

i. Has a liver problems?

P(L) = 8% or 0.08

ii. Is a heavy drinker ?

From the question, we have:

Probability of people that have liver problems and are heavy drinkers P(L & H) = 25% = 0.25

Probability of people that have do not have liver problems and are heavy drinkers P(NL & H) = 5% = 0.05

Probability ( Heavy drinker) =

P(L) × P(L & H) + P(NL) × P(NL & H)

= 0.25 × 0.08 + 0.05 × 0.92

= 0.066

iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?

Probability (Heavy drinker and has liver problem) = [P(L) × P(L & H)] ÷ [P(L) × P(L & H)] + [P(NL) × P(NL & H) ]

= [0.25 × 0.08] ÷ [0.25 × 0.08] + [0.05 × 0.92]

= 0.303030303

Approximately = 0.303

iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?

P(L & H) = 25% = 0.25

v. If a person is found to be a non –drinker, what is the probability that this person has liver problems.?

People with liver problems are non-drinkers. = P( L & N) = 40% = 0.4

People without liver problems and do not drink at all = P( NL & N) = 30% = 0.3

Probability (non drinker and has liver problem) = [P( L & N) × P(L & H)] ÷ [P( L & N) × P(L & H)] + [ P( NL & N) × P(NL & H) ]

= [0.4× 0.08] ÷ [0.4 × 0.08] + [0.3 × 0.92]

= 0.1038961039

Approximately ≈ 0.104

how many pounds are in 2 tons 1,760 ounces

Answers

Answer:

4110

Step-by-step explanation:

One ton is equal to 2000 pounds and one ounce is equal to 0.0625 pounds.

2 tons*2000 lbs per ton  = 4000 lbs

1760 ounces*0.0625 lebs per ounce = 110 lbs

4000+110=4110 lbs

Giving a test to a group of students, the grades and gender are summarized below

A B C Total

Male 19 4 12 35

Female 3 13 5 21

Total 22 17 17 56

Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.

Enter your answer as a tri-linear inequality using decimals (not percents).

< p

Answers

Answer:

Using Anova for a tri linear probability at ∝= 0.005

Step-by-step explanation:

Here simple probability cannot be used because  we want to enter your answer as a tri-linear inequality using decimals (not percents).

So we can use ANOVA

Null hypothesis

H0: µA = µB=µC

all the means are equal

Alternative hypothesis

H1: Not all means are equal.

The significance level is set at α-0.005

The test statistic to use is

F = sb²/ sw²

Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .

The computations are as follows

                     XA (XA)²            XB (XB)²         XC (XC)²       Total   ∑X²

Male                   19(361)          4(16)                 12(144)           35     521    

Female               3(9)                13 (169)           5  (25)            21      203  

TotalTj                  22                   17                      17              56     724

T²j                       (22)(22)

                             484                 289                  289        1062  

∑X²                     370               285                     169

Correction Factor = CF = Tj²/n = (56)²/6= 522.67

Total SS ∑∑X²- C. F = 724- 522.67= 201.33

Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33

Within SS = Total SS - Between SS

=201.33- 8.33= 193

The Analysis of Variance Table is

Source Of                Sum of          Mean         Computed

Variation        d.f    Squares      Squares                    F

Between

Samples           1        8.33               8.33           8.33/ 48.25= 0.1726

Within

Samples          4       193              48.25                                  

The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328

Calculated value of F = 0.1726

Since it is smaller than 5 %  reject H0.

However the decimal probability will be

Male 19 4 12 35

Female 3 13 5 21

Total 22 17 17 56

There are total 22 people who get an A but only 19 males who get an A

So the probability that a male gets an A is = 19/22= 0.8636

A coin is tossed 4 times. Let E1 be the event "the first toss shows heads" and E2 the event "the second toss shows heads" and so on. That is, Ei is the event that the "i"th toss shows up heads.
A. Are the events e e and f f independent?
B. Find the probability of showing heads on both toss.

Answers

Answer:

The events are independent.

The probability of showing heads on both toss is equal to 1/2

Step-by-step explanation:

The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.

Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.

In general the k events are defined to be mutually independent if and only if the probability of the intersection of  any 2,3,--------, k  equals the product of their respective probabilities.

P (A∩B) = P(A). P(B)

P (A∩B)   = 1/2. 1/2= 1/4

                                                                  Head          Tail

 P(E1)= 1/2  ----------          Coin 1               H,H              T,H

                                                                1/4                  1/4

  P(E2)= 1/2  ---------------  Coin 2             H, H               H,T

                                                                      1/4           1/4

So the events are independent.

The probability of showing heads on both toss is equal to 1/2

The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.

Or in other words ( 1/4* 1/4) = 2/4 = 1/2

The length of the segment between the points $(2a, a-4)$ and $(4, -1)$ is $2\sqrt{10}$ units. What is the product of all possible values for $a$? LOTS OF POINTS AND BRAINLIEST TO CORRECT ANSWER!

Answers

Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

This person made a mistake. what is the mistake and what is the correct answer?!!

Answers

Answer: 44

Step-by-step explanation:

Frank and Gregory leave Centreville traveling in opposite directions on a straight road. Gregory drives 22 miles per hour faster than Frank. After 2.25 hours, they are 216 miles apart. Find Frank's speed and Gregory's speed.

Answers

Answer:

Frank speed = 37mi/hGregory speed = 59mi/hr

Step-by-step explanation:

Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,

Speed = Distance/Time

Total time travelled by them = 2.25hours

Total distance = 216 hours

Total speed = x+y = x+22+x

Substituting this parameters into the formula given to get x we will have;

x+22+x = 216/2.25

2x+22 = 96

2x = 96-22

2x = 74

x = 74/2

x = 37

Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour

The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?

Answers

Answer:

255.8

Step-by-step explanation:

first

1/6*1535

=255.8

Isreal spends the most time on social media with a total of 11.1.peru has a total of 8.3 how much more time does israel spend on social media

Answers

Answer:

2.8

Step-by-step explanation:

11.1-8.3=2.8

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

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JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                            PEACE!

Find the particular solution of the differential equation that satisfies the initial condition(s). (Remember to use absolute values where appropriate.) f ''(x) = 4 x2 , f '(1) = 2, f(1) = 5

Answers

Looks like either [tex]f''(x)=4x^2[/tex] or [tex]f''(x)=\frac4{x^2}[/tex]...

In the first case, integrate both sides twice to get

[tex]f''(x)=4x^2\implies f'(x)=\dfrac43x^3+C_1\implies f(x)=\dfrac13x^4+C_1x+C_2[/tex]

Then the initial conditions give

[tex]f'(1)=2\implies 2=\dfrac43\cdot1^3+C_1\implies C_1=\dfrac23[/tex]

[tex]f(1)=5\implies 5=\dfrac13\cdot1^4+C_1\cdot1+C_2\implies C_2=4[/tex]

so that the particular solution is

[tex]f(x)=\dfrac{x^4}3+\dfrac{2x}3+4[/tex]

If instead [tex]f''(x)=\frac4{x^2}[/tex], we have

[tex]f''(x)=\dfrac4{x^2}\implies f'(x)=-\dfrac4x+C_1\implies f(x)=-4\ln|x|+C_1x+C_2[/tex]

[tex]f'(1)=2\implies 2=-\dfrac41+C_1\implies C_1=6[/tex]

[tex]f(1)=5\implies 5=-4\ln|1|+C_1\cdot1+C_2\implies C_2=-1[/tex]

[tex]\implies f(x)=-4\ln|x|+6x-1[/tex]

PLEASE FAST 40 POINTS

A box contains four tiles, numbered 1,4.5, and 8 as shown.

Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.

What is the probability that the sum of the two chosen tiles is greater than 7?

A. 1/4
B. 5/16
C. 2/3
D. 11/16

Answers

Answer:

[tex]\bold{\dfrac{11}{16}}[/tex]

Step-by-step explanation:

Given four tiles with numbers:

1, 4, 5 and 8

Tile chosen once and then replaced, after that another tile chosen:

All possibilities are:

{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)

(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)

(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Total number of possibilities = 16

When the sum is greater than 7, the possibilities are:

{(1, 8)

(4, 4) ,(4, 5) ,(4, 8)

(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Number of favorable cases = 11

Formula for probability of an event E is:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Hence, the required probability is:

[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]

Answer:11/16

Step-by-step explanation:i took the test

Which of the following describes a situation in which the total distance a ball travels is zero meters from its starting point? (5 points)
a
b
The ball first bounces up to a height of 4 meters, and then falls 2 meters towards the ground.
The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground.
The ball first bounces up to a height of 2 meters, and then falls 4 meters towards the ground.
The ball first bounces up to a height of 4 meters, and then falls 0 meters towards the ground.
С
d

Answers

Answer:

The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground

Step-by-step explanation:

How do i do this equation
-3(-2y-4)-5y-2=

Answers

Answer:

Step-by-step explanation: distribute -3 to the parenthesis (-2y-4) to eliminate the parenthesis. you’ll be left with 6y +12 -5y-2. From there you combine like terms. do 6y-5y= 1y or just y and 12-2 = 10. your answer would be 10

Halla x si:

a) 4√5 b) √5 c) 4√3 d) 4 e) 4√2

Answers

Answer:

Option A. 4√5

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y as shown in the attached photo.

The value of y can be obtained by using the pythagoras theory as illustrated below:

In this case y is the longest side i.e the Hypothenus.

y² = 4² + [4√3]²

y² = 4² + [4² × (√3)²]

y² = 4² + [4² × 3]

y² = 16 + [16 × 3]

y² = 16 + 48

y² = 64

Take the square root of both side

y = √64

y = 8

Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.

Note: x is the longest side i.e the Hypothenus in this case.

x² = 4² + 8²

x² = 16 + 64

x² = 80

Take the square root of both side

x = √80

x = √(16 × 5)

x = √16 × √5

x = 4√5

Therefore, the value of x is 4√5.

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*Please Show Work*​

Answers

Hi there! :)

Answer:

y = -2x + 3

Step-by-step explanation:

We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in values from the table:

[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]

Simplify:

m = -2 (rate of change)

Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:

7 = -2(-2) + b

7 = 4 + b

7 -4 = b

b = 3

Rewrite:

y = -2x + 3 is the equation for the linear function.

I dont understand how to do this

Answers

Answer:

Put 25 in the box.

Step-by-step explanation:

Apply the exponent rule: (ax)^n = a^n × x^n

So we have:

(5x)^2 = 5^2 × x^2

= 25x^2

Best Regards!

A tin of tennis balls costs $6.99, and each tin contains 4
tennis balls.
If the tennis balls were sold individually, then
approximately how much would one tennis ball cost?
$​

Answers

Answer:

About $1.75 per tennis balls

Step-by-step explanation:

A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.

We need to find the unit price, or price per ball.

Divide the cost by the number of tennis balls.

cost / tennis balls

cost = $6.99

tennis balls = 4 tennis balls

$6.99 / 4 tennis balls

Divide 6.99 by 4.

$1.7475 / 1 tennis ball

Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.

$1.75 / 1 tennis ball

It would cost approximately $1.75 for one tennis ball.

Help me solve this!!!

Answers

Answer:

m∠AOD = 140°

Step-by-step explanation:

In the diagram attached,

OA⊥OC and OB⊥OD

m∠AOD = 3.5(m∠BOC)

Since, m∠BOD = 90°  [Given: OA⊥OC]

m∠BOC + m∠COD = 90° ---------(1)

Similarly, m∠AOC = 90° [Given : OA⊥OC]

m∠AOB + m∠BOC = 90° --------(2)

Equation (1) - Equation(2)

(m∠BOC + m∠COD) - (m∠AOB + m∠BOC) = 90°- 90°

m∠COD = m∠AOB

m∠AOB + m∠BOC + m∠COD = m∠AOD --------(3)

m∠AOB + m∠BOC + m∠AOB = 3.5(m∠BOC) [Since m∠COD = m∠AOB]

2m∠AOB = 3.5(m∠BOC) - m∠BOC

2m∠AOB = 2.5(m∠BOC)

m∠AOB = 1.25(m∠BOC)

From equation (2),

m∠AOB + m∠BOC = 90°

1.25(m∠BOC) + m∠BOC = 90°

2.25(m∠BOC) = 90°

m∠BOC = 40°

From equation (1),

m∠BOC + m∠COD = 90°

m∠COD + 40° = 90°

m∠COD = 50°

Now by putting these values in equation (3)

m∠AOB + m∠BOC + m∠COD = m∠AOD

m∠COD + m∠BOC + m∠COD = m∠AOD

50° + 40° + 50°= m∠AOD

m∠AOD = 140°

jana has 3 banana muffins, 3 poppy seed muffins, 3 spice muffins and 3 blurry muffins she put 1/2 of the muffins on a late how many muffins did janna put on the plate

Answers

Answer:

  6

Step-by-step explanation:

Jana had a total of 3+3+3+3 = 12 muffins. Half that number is 3+3 = 6 muffins.

Jana put 6 muffins on the plate.

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