7. If f(x) = -3x² + 2x - 1 and f(x) = -1, solve for x.

The probability of getting 2 yellow apples and 1 red apple is 18/35 which is the D option.

This is a question of permutations and combinations.

Given that:-

Number of yellow apples = 4

Number of red apples = 2

We have to find the probability of getting 2 red apples and 1 yellow apple.

Number of ways of getting 2 yellow apples = [tex]^4C_2=6[/tex]

Number of ways of getting 1 red apple = [tex]^3C_1=3[/tex]

Total number of ways of finding 3 apples from 7 apples = [tex]^7C_3=35[/tex]

Hence,

Probability of getting 2 yellow apples and 1 red apple = 6*3/35 = 18/35.

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[tex]T(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{3}{5}}(x-\stackrel{x_1}{4}) \\\\\\ y-1=\cfrac{3}{5}x-\cfrac{12}{5}\implies y=\cfrac{3}{5}x-\cfrac{12}{5}+1\implies {\Large \begin{array}{llll} y=\cfrac{3}{5}x-\cfrac{7}{5} \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line AB

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3 }{ 4 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-3}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{-3}\implies \cfrac{4}{3}}}[/tex]

so we're really looking for the equation of a line that has a slope of 4/3 and that it passes through (3 , 2)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=\cfrac{4}{3}x-4\implies {\Large \begin{array}{llll} y=\cfrac{4}{3}x-2 \end{array}}[/tex]

The ratio sinC is given by 4/5 and in decimal form is given by sinC = 0.8.

The trigonometric functions are real functions in mathematics that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic events.

The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals. These six trigonometric functions each have an analog in the hyperbolic functions, as well as an equivalent inverse function.

The value of sin C is given by

sinC = perpendicular/ hypotenuse

sinC = AB/AC

sinC = 4/5

In decimal form, it is written as

sinC = 0.8

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[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]

The graph of the function  y=3 -1/2x is attached below.

Function:

Function refers the relationship between inputs where each input is related to exactly one output.

Given,

Here we have the function  y=3 -1/2x.

Now, we have to plot the graph of the function.

In order to plot the graph of the function, we have to take some sample values for x.

So, we will take the values of the x as -2, -1, 0, 1, 2.

Now, we have to apply the values on the given function then we get,

=> x = -2 => y = 3 - 1/2(-2) => y = 3 + 1 => y = 4

=> x = -1 => y = 3 - 1/2(-1) => y = 3 + 1/2 => y = 7/2 = 3.5

=> x = 0 => y = 3 - 1/2(0) => y = 3 - 0 => y = 3

=> x = 1 => y = 3 - 1/2(1) => y = 3 - 1/2 => y = 5/2 = 2.5

=> x = 2 => y = 3 - 1/2(2) => y = 3 - 1 => y = 2

When we enter these values into the table, then we get the table like the following.

By using the table we have to plot the graph and then we get the graph like the following.

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The solution after divide by 8/5 instead of 4/5 will be 2.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The model shows that 3 1/5 divided by 4/5 = 4.

Now,

Substitute 8/5 instead of 4/5, we get;

⇒ 3 1/5 ÷ 8/5

⇒ 16/5 ÷ 8/5

⇒ 16/5 × 5/8

⇒ 2

Thus, The solution after divide by 8/5 instead of 4/5 will be 2.

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Answer:

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

PEMDAS!

1) 20/2 = 10

2) 10*5+8

3) 10*5 = 50
4) 50 + 8 = 58

Answer is 58, hope this helps ;)

The ratio of c and 10 is c:10.

According to the question,

We have the following information:

We have one variable and one number which are c and 10 respectively.

Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.

(For example, x can not be divided by 20.)

So, we will replace the sign of division by that of the ratio.

c/10

c:10

Hence, the ratio of c and 10 is c:10.

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The variation equation that connects x and y is y³ = 4.5x(x - 1) and the value of y is 4.48 when x equals  5

From the question, the variation statement is given as

The cube of y is directly proportional to x(x - 1)

Also, we have the initial values of x and y to be

x = 3 and y= 3

When the variation statement is represented as an equation, we have:

y³ = kx(x - 1)

Where k is the variation constant

Substitute the known values in the above equation So, we have the following equation

3³ = k x 3 x (3 - 1)

Evaluate

27 = 6k

Divide both sides by 6

k = 4.5

Substitute k = 4.5 in y³ = kx(x - 1)

y³ = 4.5x(x - 1)

Hence, the equation is y³ = 4.5x(x - 1)

Here, we are given that

x = 5

Substitute 5 for x in the equation y³ = 4.5x(x - 1)

So, we have

y³ = 4.5 x 5 x (5 - 1)

Evaluate

y³ = 90

Take the cube root of both sides

y = 4.48

Hence, the value of y is 4.48

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The temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

The process of converting a temperature value from one unit to another is known as temperature conversion. On scales like Kelvin, Celsius, Fahrenheit, etc., we measure temperature. The freezing point and boiling point of water, respectively, are 273.15K and 373.15K on the Kelvin scale. The freezing point and boiling point of water, respectively, are 32°F and 212°F on the Fahrenheit scale. The freezing point and boiling point of water, respectively, are 0°C and 100°C on the Celsius scale.

Given, The hottest day recorded in Oklahoma was 120° Fahrenheit

F=(9/5)C+32

120=(9/5)C+32

(9/5)C=88

C=48.89

Therefore, the temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

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Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 6.

I got this by subtracting 23 by 12 (the number of numbers shown). Then I got 11. So I followed the pattern until I got six.

23-12=11

2,4,6,8,2,4,6,8,2,4,6,8,......2,4,6,8,2,4,6,8,2,4,6

The number of times Aarf the Dog bark for 15 seconds if the dog starts barking at midnight and stops at 1:01 AM is 91.5 times

Total time of barking and silence = 15 seconds + 25 seconds

= 40 seconds

Difference in time = 1:01 AM - 12:00 am

= 1 hour 1 minutes

Convert hours and minutes to seconds

1 hour 1 minutes = 61 minutes × 60 seconds

= 3,660 seconds

Number of times Aarf the Dog bark for 15 seconds = Total hours Aarf dog barks / Total time of barking and silence

= 3,660 / 40

= 91.5 times

So therefore, the number of Aarf the Dog bark for 15 seconds is 91.5 times

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Step-by-step explanation:

as the graph shows :

4x + 12x = 320

16x = 320

x = 20

The probability that Halima walks at least one way is 0.64

Calcualting Probability:

Probability is a branch of mathematics which is deals with the occurrence of a random event. The value of probability is expressed from zero to one but not more than 1. It is used to predict how likely events are to happen. The probability of an event 'E' is denoted by P(E).

Here we have

Halima either travels by bus or walks when she visits the town center

The probability that she catches the bus to town = 0.4

The probability that she catches the bus from town = 0.9

Let A and B be the events that she catches the bus to the town and the event that she catches the bus from the town respectively

=> P(A) = 0.4

=> P(B) = 0.9

The above events P(A) and P(B) are two independent events

Then the probability that she catches the bus to and from the town
=> P(A∩B) =  0.4 × 0.9 = 0.36

Therefore,

The Probability she walks at least one way P(A ∪ B) = 1 - P(A∩B)
=> P(A∪B) = 1 - 0.36

=>  P(A∪B) = 0.64

Hence,

The probability that Halima walks at least one way = 0.64

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Answer: 0.4754

A poker hand is a combination of 5 cards from the pack of 52 cards.

One hand full is said when we have 2 cards of the same rank.

In this question, we have to find the probability of 2 hands full of different ranks.

So,

We use the formula : C(n,k)=\frac{n!}{k!(n-k)!}

From permutations and combinations, since order doesn't exist.

From a suit of 13 cards any two cards are chosen:

C(13,2)=\frac{13!}{2!(13-2)!}

C(13,2)=\frac{13×12×11!}{2!11!}

C(13,2)=\frac{13×12!}{2!}

C(13,2)=156/2

C(13,2)=78

78 ways are there to choose for each of the pairs .

Now,

If one of the ranks is of any particular suit or maybe a face card out of which two of them are chosen.

C(4,2)=\frac{4!}{2!(4-2)!}

C(4,2)=6

And same for the other sets of cards of another pair.

We have 78×6×6= 2808 ways to pick the first 4 cards.

Now,

For the fifth card which can be any card except for the paired suit i.e, 13-2=11

There are 4 suits to pick from, 4×11= 44 cards to pick for the final card.

For the first card = 2080

For the fifth card= 44

Total number of two pair hands possible= 2080×44= 123,552

Out of:

C(52,5)=\frac{53!}{5!(52-5)!}

C(52,5)= 2,598,960

Probability of event= 123,552/2,598,960

= 0.4753901560624

Final answer= 0.4754

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The probability of being dealt a two-pair is 0.4754.

Given;

What is the likelihood of receiving a two-pair when dealing a five-card poker hand from a 52-card deck that has been properly shuffled?

We use combinations to solve the given case;

From each suit, any two cards are chosen,

C(13,2) = [tex]\frac{13!}{2!(13-2)!}[/tex]

           = [tex]\frac{13*12*11!}{2!11!}[/tex]

           = 156/2

           = 78

Hence, there are 78 ways to choose for each of the pairs.

Now,

If one of the ranks is a face card, two of them are chosen, or if one of the ranks is a certain suit.

C(4,2) = [tex]\frac{4!}{2!(4-2)!}[/tex]

          =6

Similar to the other sets of cards of another pair.

We have 78×6×6= 2808 ways to pick the first 4 cards.

Now,

The fifth card, which can be any card other than the paired suit, is dealt as follows: 13 - 2 = 11.

There are 44 cards total to choose from among the 4 suits, or 4 x 11.

2080 for the primary card.

44 for the fifth card.

Possible two-pair hands total 2080 x 44 = 123,552.

Then,

C(52,5) = [tex]\frac{53!}{5!(52-5)!}[/tex]

            = 2,598,960

Probability of event = Possible two-pair hands / Total outcome

                                 = 123,552 / 2,598,960

                                 = 0.47539

Hence, the probability of being dealt a two-pair is 0.4754.

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The probability that a card drawn randomly from a standard deck of 52 cards is a red queen is 1/26 or 0.038461. The result is obtained from the ratio of the number of red queen to 52 cards.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

In case a card drawn randomly from 52 cards, what is the probability that it is a red queen?

The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

From that information, the number of red queen in a standar deck of 52 cards is 2 cards. So,

The probability of drawing a red queen is

P(A) = n(A) / n(S)

P(A) = 2/52

P(A) = 1/26

P(A) = 0,038461

Hence, the probability that a card drawn is a red queen is 1/26 or 0,038461.

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Answer:

Step-by-step explanation:

firstv= block second one

secondblock third one

and so on

Answer:

[tex]r = 2279.41[/tex]

A. The correlation coefficient is of 0.303.

B. There are six positive and four negative.

C. The point with the largest residual is (6,2).

By choosing the points (x,y) from the scatter plot and entering them into a calculator, the correlation coefficient can be calculated.

A) The coordinates of these points are:

(1,2), (1,3), (2,4), (3,4), (3,5), (4,3), (4,5), (5,5), (5,6), (6,2).

Now, using Pearson correlation we have

X Values:

∑ = 34

Mean = 3.4

∑(X - Mx)² = SSx = 26.4

Y Values:

∑ = 39

Mean = 3.9

∑(Y - My)² = SSy = 16.9

So, when X and Y Combined

N = 10

∑(X - Mx)(Y - My) = 6.4

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 6.4 / √((26.4)(16.9))

r= 0.303

Hence, the correlation coefficient is 0.303

B) As, The difference between the observed value and the expected value, or residual, is determined as follows:

C) The largest residual using absolute value is at the point is (6,2).

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The value of their horizontal change is 2.7 feet

The equation of the function is given as

y = -8/3x + 40

From the question, the distance travelled by the rider is given as

Distance = 8 feet downward

This means that

Horizontal change = slope

A linear equation is represented as

y = mx + c

Where

Slope = m

By comparing y = mx + c and y = -8/3x + 40, we have

Slope = m = 8/3

This gives

Horizontal change = 8/3

Evaluate

Horizontal change = 2.7

Hence, the horizontal change is 2.7 feet

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For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.

The assortment of bags weighs 19.7 pounds on average.

3.1 pounds is the standard deviation.

The sampling distribution theorem and the normal probability density function were both utilized.

The z-score formula is used to address problems involving samples with regularly distributed data.

Mean standard deviation, the z-score of a measure X is given by:

z = (x - μ) ÷ σ

The Z-score computes the number of standard deviations. The metric used is the average.

After calculating the Z-score, we look at the p-value associated with it in the z-score table.

This p-value represents the probability that the measure's value is smaller than X, or the percentage of X.

By taking away 1, we can determine the chance that the measure surpasses X.

If n is at least 30, the Central Limitation Theorem can also be applied to variables that are skewed.

No of the sample size, the sample mean will always be the same.

However, the standard error will change.

P(a > 22) denotes the likelihood that the sample means will be greater than 22.

The likelihood that they give it a chance will weigh more than 22 pounds is around 0.05 for all sampling of size 5.

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Answer:

[tex]y=-\frac{2}{3}x-2[/tex]

Step-by-step explanation:

To find the equation in slope-intercept form, isolate [tex]y[/tex].

[tex]2x+3y=-6 \\ \\ 3y=-2x-6 \\ \\ y=-\frac{2}{3}x-2[/tex]

Based on the information, the person traveled 117.8 feet by the Ferris wheel.

Circumference = π×diameter

Keep the values in formula and perform multiplication to find the circumference of the wheel

Circumference = 50π

On 1 complete revolution of 360 degrees, the distance covered = 50π

So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270

Performing multiplication and division on Right Hand Side of the equation

The distance traveled = 117.8 feet

Hence, the person travelled 117.8 feet.

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Answer:

SAS

Step-by-step explanation:

∠CBA ≌ ∠DBA are equal by SAS

Answer:

X = 1

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

To solve for x we should try to isolate the x by itself so :

Let's add 3 to both sides :

2x-3 + 3 = 1 + 3

-3+3 = 0

2x(+0) = 4

2x = 4

Divide both sides by 2 so we have just x on its own :

2x÷2 = 4÷2

x = 2

Let's check by putting this x value in the question :

2(2)-3 = 1

2(2) = 2×2 = 4

4 - 3 = 1

1 = 1

✅

So x = 2

Hope this helped and have a good day

Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter