50 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 31 pupils use the swimming pool. 28 pupils use the gym. 7 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:h(x) = - \cfrac{1}{3} x + 2[/tex]

we need to find -4 h(9) :

[tex]\qquad❖ \: \sf \: - 4 \: h(9)[/tex]

[tex]\qquad❖ \: \sf \: - 4 \bigg(- \dfrac{1}{3} \times 9 + 2 \bigg)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 3 + 2)[/tex]

[tex]\qquad❖ \: \sf \: - 4( - 1)[/tex]

[tex]\qquad❖ \: \sf \:4[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: - 4 \: h(9) = 4[/tex]

Answer:

x=1990

Step-by-step explanation:

x+10=2000

x=2000-10

x=1990

Answer:

therefore x = 1990

Step-by-step explanation:

x+10 = 2000

= x = 2000-10

= x = 1990

Answer:

110 degrees

Step-by-step explanation:

to find the angle x, we need to use the formula to find the 50 degree angle:

(y - x) / 2 = 50

y is 210

(210 - x) /2 = 50

210-x = 100

x = 110 degrees

Answer:

7/14, so 50%

Step-by-step explanation:

A one-tailed test's p-value is half that of a two-tailed test.

Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.

Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

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Answer: 6/23  mph

Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.

Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.

Y assume we have an exponential equation of the form:

y = a*b^x + c

In this case, a is what we know as the "initial value" of the exponential.

Notice that when we evaluate in x = 0, we get:

y = a*b^0 + c

y = a + c

So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.

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Given :-

Solution :-

>> 2x + 5 < x + 1 / 4

>> 4 (2x + 5) < x + 1

>> 4 × (2x + 5) < x + 1

>> 8x + 20 < x + 1

>> 8x - x < 1 - 20

>> 7x < 1 - 20

>> 7x < -19

>> x = -19 / 7

[tex]\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}[/tex]

Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.

          [tex]\boldsymbol{\sf{8x+20 < x+1 }}[/tex]

Resta x en los dos lados.

              [tex]\boldsymbol{\sf{8x+20-x < 1 }}[/tex]

Combine 8x and −x to get 7x.

                [tex]\boldsymbol{\sf{7x+20 < 1 }}[/tex]

Subtract 20 on both sides.

                 [tex]\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}[/tex]

                  [tex]\boldsymbol{\sf{7x < -19 }}[/tex]

Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.

                     [tex]\boldsymbol{\sf{x < -\dfrac{19}{7} } }[/tex]

As the end result, it is not simplified or divided, then

                               [tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}[/tex]

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Answer:

t ≥ 36

Step-by-step explanation:

took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.

The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

We know that t is the time,  in minutes, since Marcel plugged in the phone and the tablet.

For phone:-

Initial battery charge = 13%.

Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.

Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.

For tablet:-

Initial battery charge = 25%.

Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.

Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.

We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.

Since the phone is required to have at least as much battery charge as the tablet, we can show this as:

The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,

or, 13% + t(2/3)% ≥ 25% + t(1/3)%,

or, t(2/3)% - t(1/3)% ≥ 25% - 13%,

or, t(1/3)% ≥ 12%,

or, t ≥ 12%/(1/3)%,

or, t ≥ 36.

Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

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Statements that describe the given function are:

To find the statements that describe the given function:

Lastly, the correct answers are:

Therefore, statements that describe the given function are:

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The complete question is given below:

Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.

(A) f(x) has one real zero because it crosses the x-axis once.

(B) f(x) has two real zeros because it crosses the x-axis twice.

(C) f(x) has real zeros at 1 and –1.

(D) f(x) has a real zero at 2.5.

(E) f(x) has x-intercepts at (1, 0) and (–1, 0).

(F) f(x) crosses the x-axis when x = 1 and x = –1.

(G) f(x) has an x-intercept at (2.5, 0).

The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.

It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.

In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.

Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.

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Answer:

27/31

Step-by-step explanation:

FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31

The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.

Volume of the cylinder = [tex]\pi r^{2}h[/tex]

Rate of change of height is  [tex]\frac{dh}{dt}[/tex] = ?

At any time t,

Volume, V =  [tex]\pi r^{2}h[/tex]

Since r does not change with time, then r is a constant, so,

V =  [tex]\pi (6)^{2}h[/tex]

V = [tex]36\pi h[/tex]

Differentiate both sides with respect to time t,

[tex]\frac{dV}{dt} = 36\pi \frac{dh}{dt}[/tex] -------------(i)

Since [tex]\frac{dV}{dt}[/tex]is given as 4[tex]\pi[/tex] cu.in. per min,

[tex]4\pi = 36\pi \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{4\pi }{36\pi }[/tex]

[tex]\frac{dh}{dt} = \frac{1 }{9 }[/tex] in/min.

Hence, The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

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The correct option B.

The value of the zeros of function g is -6 and 7

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

The factors are  (x − 7) and (x + 6)

On simplifying the we get:

x²+ 6x -7x -42 = 0

x² - x - 42 = 0

The factorizing these equation we get.

So the zeros are -6 and 7 , so option b is correct.

[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]

[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]

[tex]x_1,_2[/tex] = ((1) ± 13)/2.1

[tex]x_1[/tex]    = (1+13)/2.1

[tex]x_2[/tex]     = (1 - 13)/2.1

[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6

The Zeros of the function are: (7 , -6)

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Answer:

Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?

The Answer Is X = 20 or x = 4

The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]

and z = r

A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.

Given:

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

By applying two more row operations, we get

[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]

simplifying the above matrix, we get

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]

[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and

z = r

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Based on the fact that the identical darts were thrown at four identical dartboards and Ben took a list, the number of different lists possible is 5 lists.

If all the darts hit on dartboard then the list would be:

= 0004

If one dart hit a dartboard and three hit one dartboard the list would be:

= 0031

If two darts hit two boards:

= 0022

If two darts hit one board, 1 dart two others:
= 0211

If all darts hit separate boards;

= 1111

This means that 5 lists are possible to Ben.

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Answer:

  d.  x = 5

Step-by-step explanation:

Chords that subtend congruent arcs are congruent.

Chord lengths are the same:

  AB = CD

  16x -2 = 14x +8

  2x = 10 . . . . . . add 2-14x

  x = 5 . . . . . . . . divide by 2

The annual interest paid on the account is $75

The formula for determining annual interest is given as;

Interest = PRT/100

where;

Substitute the values

Annual Interest = 1000 × 7. 5 × 1/ 100

Annual interest = 7500/ 100

Annual interest = $75

Thus, the annual interest paid on the account is $75

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Answer:

b=67.5°

Step-by-step explanation:

hope it helps!!!

Answer: try 35

Step-by-step explanation:

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k  is this series written in sigma notation.

What is the series written in sigma notation?

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k

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Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.

The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

A line segment that divides an angle into two equal parts is referred to as an angle bisector.

From the proof given, we know that;

m∠DEK = 2(m∠DEF)

m∠DEK = 2(44) = 88°

With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.

Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.

Then, KF = 1/2(DK) = 1/2(16) = 8.

The complete proof is show in the image attached below.

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Answer:

C. 206 unit^2.

Step-by-step explanation:

Area = 2*11*5 + 2*11*3 + 2*3*5

         = 110 + 66 + 30

         =  206.

Answer:

y = 56/3

Step-by-step explanation:

We need to write equations to solve

Let the two numbers be x and y

The sum is 56

x+y = 56

The first number is 2 times greater than the second number.

x = 2*y

Substitute this into the first equation

x+y = 56

2y+y=56

3y = 56

y = 56/3

Step-by-step explanation:

Let the numbers be x and y

The sum of the two numbers is 56 :

Step 1:

X + Y = 56.......... (1)

Also, the first number is 2 times greater than the second number:

Step 2:

2X + Y = 0........... (2)

By substitution method, make Y the subject from (2)

Step 3:

Y = -2X .......... (3)

Put (3) into (1)

Step 4

X - 2X = 56

-X = 56

[tex] \frac{ - x}{ - 1} = \frac{56}{ - 1} [/tex]

X = -56

Put X=56 into (3)

Step 5

[tex]y = - 2( - 56)[/tex]

[tex]y = 112[/tex]

The second number is now 112.

The purpose of statistical inference population based upon information obtained from the sample.

statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.

The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.

We have four ideas for using the statistical inference.

1. Estimating uncertainty.

2. Confidence intervals.

3. Hypothesis tests.

4. Connections with other material.

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The given question is not complete.

The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.

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The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:

The smallest 3-digit base-11 number is 100

When converted to base 10, the equivalent number is 121

The largest 3-digit base-9 number is 888

When converted to base 10, the equivalent number is 728

So, the total number of possibilities is:

Possibilities = 728 - 121 + 1

Possibilities = 608

The count of base 10 3-digit numbers is

Count = 999 - 100 + 1

Count = 900

The required probability is:

P = 608/900

Evaluate

P = 0.6753

Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753

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Complete question

A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals

Answer:

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}

Step-by-step explanation:

Tossing a coin has two possible outcomes, heads (H) and tails (T).

Spinning the spinner has 5 possible outcomes, 1, 2, 3, 4, 5.

Table:

First spin                   H     H     H     H     H    T     T     T     T     T

Second spin              1      2      3     4      5     1     2     3     4     5

Sample space:

{(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5)}