Rita's school is 5 kilometers west of her house and 5 kilometers south of her friend Jayce's
house. Every day, Rita bicycles from her house to her school. After school, she bicycles from
her school to Jayce's house. Before dinner, she bicycles home on a bike path that goes
straight from Jayce's house to her own house. How far does Rita bicycle each day? If
necessary, round to the nearest tenth

The value of y is 2 * √3.

In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.

Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.

Using trigonometric ratios, we can relate the sides of a right triangle as follows:

sin(angle) = opposite/hypotenuse

In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:

sin(45 degrees) = √2 / h

By rearranging the equation, we can solve for h:

h = √2 / sin(45 degrees)

Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:

h = √2 / (1/√2) = √2 * √2 = 2

Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:

y = 2 * √3

Therefore, the value of y is 2 * √3.

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Answer:

  B.  2

Step-by-step explanation:

You want the predicted number of missed shots after 8 weeks if the trend line equation is ...

  y = -1/2x +6

Using x=8 in the given equation, we find the prediction to be ...

  y = -1/2(8) +6 = -4 +6 = 2

The number of missed shots is predicted to be 2.

__

Additional comment

We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.

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The classification of the given polynomial is cubic polynomial, the correct option is C.

We are given that;

The equation=3x^3-x^2-x+4

Now,

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Degree of 3x^3=3

Degree of x^2=2

Degree of x=1

The heighest degree of the polynomial is three of 3x^3.

Therefore, by the polynomial the answer will be cubic polynomial.

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Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

Answer:

1) 5/6
2) 19/30
3) They are mutually exclusive.

Step-by-step explanation:

Let's break the diagram down.
We have four types of smoothies:

Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8

From here, we find that there are 30 smoothies in total.

In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.

Therefore,

[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]

Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.

[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]

We can check if the events are mutually exclusive using the formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).

[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.

If the two sides are equal, the cases are not mutually exclusive.

[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]

Therefore, the events are mutually exclusive.

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]

[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]

Step-by-step explanation:

Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].

According to the problem: [tex]b = \frac{2}{5} \times g[/tex]

We also know that the total number of students is 42, so [tex]b + g = 42[/tex].

Now, we have two equations with two variables:

We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].

Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]

From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]

Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation

Replace [tex]b[/tex] in the second equation with the expression we found in step 1.

[tex]\frac{2}{5} \times g + g = 42[/tex]

Step 3: Solve for [tex]\bold{g}[/tex]

Now, we have an equation with only one variable, [tex]g[/tex]:

[tex]\frac{2}{5} \times g + g = 42[/tex]

To solve for [tex]g[/tex], first find a common denominator for the fractions:

[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]

Combine the fractions:

[tex]\frac{7}{5} \times g = 42[/tex]

Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:

Step 4: Find the value of [tex]\bold{b}[/tex]

Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:

So, there are 12 boys and 30 girls in the class.

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x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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The angle relationship between DCA and BCA is that they are congruent.

In Mathematics and Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

Generally speaking, the diagonals of a rhombus are angle bisectors. In this context, we can logically deduce that the two (2) angles that would result from the bisection of angle C by a straight line are congruent.

By applying the angle bisector theorem to the given square sign (rhombus ABCD) below, we would have the following congruent angles;

∠DCA ≅ ∠BCA

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The end behavior of the graph of the function f(x) = -5(4x - 2) as x approaches infinity can be described as follows:

As x approaches infinity (or positive infinity), the value of 4x becomes infinitely large compared to the constant -2. Therefore, we can ignore the constant (-2) and simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will decrease without bound as x approaches infinity. In other words, the function will approach negative infinity (or -∞) as x becomes infinitely large.

Similarly, as x approaches negative infinity, the value of 4x becomes infinitely large in the negative direction. Thus, we can simplify the function as f(x) = -5(4x) = -20x.

Since the coefficient of x is negative (-20), the graph of the function will also decrease without bound as x approaches negative infinity. Therefore, the function will approach negative infinity (or -∞) as x becomes infinitely negative.

The average speed of Sophie in miles per hour is 5.04 miles per hour.

The speed in feet per second is 7.39 feet per second.

Given that,

Sophie recently ran a marathon.

It took her 5.2 hours to run the 26.2 miles required to complete a marathon.

Total distance ran = 26.2 miles

Total time taken = 5.2 hours

Speed = Total distance / Total time

           = 26.2 / 5.2

           = 5.04 miles per hour

Speed in feet per second = (5.04 × 5280 feet) / 3600 seconds

                                           = 7.39 feet per second

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There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Answer:

the number of meters in the milky way

Step-by-step explanation:

becuse the world is infinite

Answer:

$120

Step-by-step explanation:

Job1:

       To find the tax, multiply the payment per week ($70) by 0.1.

         Tax = payment * tax rate

                = 70 * 10%

                [tex]\sf = 70 * \dfrac{10}{100}\\\\ = \$7[/tex]

Now, to find his earning after deduction of tax, subtract 7 from 70.

Amount after deduction of tax = 70 - 7

                                                  = $ 63

Job2:

       Tax = 60 * 5%

              = 60 * 0.05

               = $3

  Amount after deduction = 60 - 3

                                           = $ 57

Total amount Byron takes home = 63 + 57

                                                      = $120

The nth roots of perfect nth powers evaluates to:

[tex]\sqrt[5]{-32}[/tex] = -2

[tex]-\sqrt[4]{256}[/tex] = -4

Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.

The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.

To find the nth roots of perfect nth powers with signs, you can use the following steps:

1. Write the perfect nth power as a product of nth roots.

2. Find the nth root of each factor.

3. Combine the nth roots to get the final answer.

[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]

         = -2

-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]

           = -4

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Answer:

x = 8 and y = -4

Step-by-step explanation:

3x + 4y = 8    (call this equation '1')

x - y = 12      (call this '2')

multiply '2' by 3:

3x - 3y = 36  (call this '3')

subtract '1' from '3':

(3x - 3y = 36)  -  (3x + 4y = 8)

0x + -7y = 28

-7y = 28

y = -4.

sub that back into '1':

3x + 4y = 8

3x + 4(-4) = 8

3x - 16 = 8

3x = 8 + 16 = 24

x = 8.

sub both y =-4 and x =8 into '2' to check if everything adds up:

x - y = 12

8 - -4 = 8 + 4 = 12

so x = 8 and y = -4

Answer:

To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:

B(1985) = -328.2 * 1985 + 13716

B(1985) = -648537 + 13716

B(1985) = 7122

So, there were approximately 7122 federally insured banks in 1985.

The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."

The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."

The meaning of ran R = { v : there exist u, (u, v) ∈ R} is,

⇒ Defined as v, there exist u such that an order pair (u, v) is belon in relation R

We have to given that;

The meaning of,

⇒ ran R = { v : there exist u, (u, v) ∈ R}

Since, WE know that;

''ran R'' is stand for range of relation R.

Which is defined as,

⇒ ran R = { v : there exist u, (u, v) ∈ R}

That's mean,

Let us defined as v, there exist u such that an order pair (u, v) is belon in relation R.

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Answer:

–6x – 3

Step-by-step explanation:

To find the expression that is equivalent to 3(–2x – 1), we need to distribute the 3 to each term inside the parentheses.

When we distribute 3 to –2x, we get:

3 * –2x = –6x

When we distribute 3 to –1, we get:

3 * –1 = –3

Therefore, the expression equivalent to 3(–2x – 1) is:

–6x – 3.

Answer:

-6x - 3

Step-by-step explanation:

Distribute 3 through the parenthesis:

[tex]\sf{3(-2x-1)}[/tex]

[tex]\sf{3*(-2x)+3*(-1)}[/tex]

[tex]\sf{-6x-3}[/tex]

Hence, the expression that is equivalent  to 3(-2x - 1) is -6x - 3.

The solution of the System of equation are,

⇒ x = 1

⇒ y = 5

We have to given that;

System of equation are,

⇒ 3x - 5y = - 22

⇒ 4x + 2y = 14

Now, We can simplify as;

From (ii);

2x + y = 7

y = 7 - 2x

Put above value in (i);

3x - 5 (7 - 2x) = - 22

3x - 35 + 10x = - 22

13x = - 22 + 35

13x = 13

x = 1

From (i);

⇒ 3x - 5y = - 22

⇒ 3 - 5y = - 22

⇒ 3 + 22 = 5y

⇒ 25 = 5y

⇒ y = 5

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Answer:

Step-by-step explanation:

There are several reasons why a student would choose to study in a province different from their home province. Some of the reasons include:

To gain a new perspective and experience different cultures.

To take unique classes that are not available in their home province.

To learn history through immersive experiences.

To improve their ability to adapt.

To gain independence.

To gain international experience and a global network.

To immerse themselves in another language.

Answer:

[tex]-2x^{-2} \ \text{or} \ -\frac{2}{x^2}[/tex]

Step-by-step explanation:

Find [tex]\frac{d}{dx}[\frac{2}{x} ][/tex].

(1) - Pull out the constant

[tex]\frac{d}{dx}[\frac{2}{x} ]\\\\\Longrightarrow 2\frac{d}{dx}[\frac{1}{x} ][/tex]

(2) - Flip the fraction

[tex]2\frac{d}{dx}[\frac{1}{x}]\\\\\Longrightarrow 2\frac{d}{dx}[x^{-1}][/tex]

(3) - Apply the power rule]

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right}\\\\\\2\frac{d}{dx}[x^{-1}]\\\\\Longrightarrow 2[(-1)x^{-1-1}]\\\\\Longrightarrow 2[-x^{-2}]\\\\\therefore \boxed{\boxed{\frac{d}{dx}[\frac{2}{x} ] =-2x^{-2} \ \text{or} \ -\frac{2}{x^2}}}[/tex]

Thus, the problem is solved.

Answer:

[tex]\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300[/tex]

Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.

Step-by-step explanation:

you already have a cosine. You might as well change that sine in a cosine too:

[tex]8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0[/tex]

(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace [tex]x=cos\theta[/tex] and let's solve

[tex]8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8[/tex]

At this point we're back to the replacement. We have two options

[tex]cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°[/tex]

Answer:

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

Given function:

In order to find its inverse, first swap x and y:

Then solve for y:

The inverse function is y= √x.

The measure of arc XYL + measure of arc VUL + measure of arc VIX = 360°.  Therefore, the correct answer is option D.

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference.

From the given circle, measure of arc XYL + measure of arc VUL + measure of arc VIX = 360° (Complete angle)

Therefore, the correct answer is option D.

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(a) The expected value of playing the game is 0.

(b) Heather can expect to break even in the long run.

To find the expected value of playing the game, we need to calculate the weighted average of the possible outcomes.

Expected value calculation:

The probability of selecting each ball is the same since Heather replaces the ball in the bag each time.

The probability of selecting any particular number is 1/8.

Expected value = (Probability of outcome 1 × Value of outcome 1) + (Probability of outcome 2 × Value of outcome 2) + ... + (Probability of outcome 8 × Value of outcome 8)

Expected value = (1/8 × 1) + (1/8 × 2) + (1/8 × 5) + (1/8 × 6) + (1/8 × 8) + (1/8 × 10) + (1/8 × (-13)) + (1/8 × (-13))

Expected value = (1/8) + (2/8) + (5/8) + (6/8) + (8/8) + (10/8) + (-13/8) + (-13/8)

Expected value = 26/8 - 26/8

Expected value = 0

Since the expected value of playing the game is 0 On average, she neither gains nor loses money over multiple plays of the game.

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The minimum is the smallest value in the data set:

Minimum: 4

The maximum is the largest value in the data set:

Maximum: 21

The median is the middle value in the data set. Since there are an even number of values in this data set, we take the average of the two middle values:

Median: (10 + 12)/2 = 11

To find the quartiles, we first need to find the median of the lower half and upper half of the data set:

Lower half: 4, 7, 9, 10

Upper half: 12, 15, 20, 21

Median of lower half: (7 + 9)/2 = 8

Median of upper half: (15 + 20)/2 = 17.5

The first quartile (Q1) is the median of the lower half of the data set:

1st Quartile: 8

The third quartile (Q3) is the median of the upper half of the data set:

3rd Quartile: 17.5

Therefore: Minimum: 4 Maximum: 21 Median: 11 1st Quartile: 8 3rd Quartile: 17.5

I hope this helps! Let me know if you have any other questions.

Answer:

--6a^6b^5+12a^5b^4+60a^2b^4+42ab^3

Step-by-step explanation:

Answer:

x = -6 and y =5

Step-by-step explanation:

2x + 5y = 13    (call this equation '1')

-4x - 3y = 9    (call this '2')

multiply '1' by 2

4x + 10y = 26       (call this '3')

eliminate by adding '2' and '3':

(-4 + 4)x + (-3 + 10)y = 9 + 26

7y = 35

y = 5

sub that into '1':

2x + 5(5) = 13

2x + 25 = 13

2x = 13 - 25 = -12

x = -6

sub both x = -6 and y =5 into '2' to make sure everything adds up:

-4(-6) - 3(5) = 24 - 15 = 9

so x = -6 and y = 5

Answer:

608 in²

Step-by-step explanation:

To figure out how much wrapping paper we need to cover the box, we can find its surface area.

The surface area of a rectangular prism (a box) is defined as:

[tex]SA = 2A + (P \cdot d)[/tex]

where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.

From the diagram, we can identify the following values for these variables:

[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]

[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]

[tex]d = 4\text{ in}[/tex]

Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.

[tex]SA = 2A + (P \cdot d)[/tex]

[tex]SA = 2(192) + (56 \cdot 4)[/tex]

[tex]SA = 384 + 224[/tex]

[tex]SA = 608 \text{ in}^2[/tex]

So, we need 608 in² of paper to cover the box.

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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