Look at this graph. What's the slope of the line?


a. 1/2

b. –2

c. –1/2

d. 2

Answer:

Step-by-step explanation:

[tex]\frac{1}{2}[/tex]  pound chocolate

Let x be the number of pounds of chocolate that needs to be mixed.

The cost of the chocolate is $14.60 per pound, so the cost of x pounds of chocolate is 14.6x dollars.

The cost of the trail mix is $4.40 per pound, so the cost of 12 pounds of trail mix is 4.4(12) = 52.8 dollars.

The cost of the mixture is $9.70 per pound, so the cost of (x + 12) pounds of the mixture is 9.7(x + 12) dollars.

We can set up an equation based on the fact that the total cost of the mixture equals the sum of the costs of the individual components:

14.6x + 52.8 = 9.7(x + 12)

Simplifying and solving for x, we get:

14.6x + 52.8 = 9.7x + 116.4

4.9x = 63.6

x = 12.98

Rounding to the nearest pound, we get x = 13.

Therefore, the store owner should mix 13 pounds of chocolate with 12 pounds of trail mix to create a mixture worth $9.70 per pound.

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We have eliminated the parameter from the given parametric equations:

x = cost,

y = tant,

To eliminate the parameter from the given parametric equations:

x = cost,

y = tant,

We can use the trigonometric identity:

tant = sint/cost.

Substitute the value of tant in terms of x and y using the trigonometric identity:

y = sint/x.

Rearrange the equation to solve for sint:

sint = y × x.

Substitute the value of sint back into the trigonometric identity to find the expression for cost:

[tex]cost = x / \sqrt{(1 + (y \times x)^2).}[/tex]

Therefore, by following these steps, we have eliminated the parameter from the given parametric equations:

x = cost,

y = tant,

and obtained the equations:

[tex]cost = x / \sqrt{(1 + (y \times x)^2),} \\sint = y \times x.[/tex]

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Answer:

a

Step-by-step explanation:

a

Answer:

4

Step-by-step explanation:

2120 - 4 = 2116

[tex]\sqrt{2116} =46[/tex]

[tex]46^{2} =2116[/tex]

Hope this helps

The solution in interval notation is (-∞, -8/45).

To solve the equation 12x + 77x + 22 < 1 + 6x - 8x + 5, we can simplify both sides:

12x + 77x + 22 < 1 + 6x - 8x + 5

Combining like terms:

89x + 22 < -x + 6

89x + x < 6 - 22

90x < -16

Divide both sides by 90:

x < -16/90

Simplifying the fraction:

x < -8/45

Therefore, the solution in interval notation is (-∞, -8/45).

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The average amount the player can expect to win or lose per game over the long run. In this game, the Expected value is x/1000.

The expected value for the numbers game, we need to calculate the weighted average of the possible outcomes.

In this game, there are 1000 possible numbers that can be selected, ranging from 000 to 999. If the player selects the winning number, they win a certain amount, and if they select any other number, they win nothing.

Let's assume the amount won is $x when the winning number is selected

The probability of selecting the winning number is 1/1000 because there is only one winning number out of the 1000 possible numbers.

The probability of not selecting the winning number is 999/1000 because there are 999 other numbers that can be selected.

The expected value (EV) can be calculated using the following formula:

EV = (Amount won if winning number is selected) * (Probability of winning) + (Amount won if losing number is selected) * (Probability of losing)

In this case, the EV is:

EV = (x * 1/1000) + (0 * 999/1000)

  = x/1000

The average amount the player can expect to win or lose per game over the long run. In this game, the expected value is x/1000.

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The equivalent value of x from the exponential equation is x = 3

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the first exponent be p = 5 + 20 ( 2 )²⁻³ˣ

Let the second exponent be q = 10 ( 2⁻²ˣ ) + 5

where the values of p and q are equal

So , p = q

And , 5 + 20 ( 2 )²⁻³ˣ = 10 ( 2⁻²ˣ ) + 5

Subtracting 5 on both sides:

20 ( 2 )²⁻³ˣ = 10 ( 2⁻²ˣ )

Divide by 2 on both sides:

2( 2 )²⁻³ˣ = ( 2⁻²ˣ )

From the laws of exponents , we get

mᵃ×mᵇ = mᵃ⁺ᵇ

2⁽¹⁺²⁻³ˣ⁾ = ( 2⁻²ˣ )

The bases are equal , so the powers are also equal

1 + 2 - 3x = -2x

Adding 3x on both sides:

x = 3

Hence , the exponents are solved and x = 3

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Answer:

  about 9.91

Step-by-step explanation:

You want the standard deviation of the given data set:

  {138, 129, 145, 134, 142, 159, 153, 142, 127}

The standard deviation can be found by a suitable calculator, or by working through the formula.

  mean = (∑x)/9 = 1269/9 = 141

  mean square = (∑x²)/9 = 179813/9 = 19,979.2222...

  σ = √((mean square) -mean²) = √98.2222...

  σ ≈ 9.91

The standard deviation of this dataset is about 9.91 units.

Between 40 and 60 minutes the target heart rate strictly increasing then strictly decreasing. Therefore, option B is the correct answer.

From the given graph, in the first curve between the interval 0-10 speed is increasing,  between the interval 10-30 speed is constant and  between the interval 30-40 speed is decreasing.

In the second curve between the interval 40-50 speed is increasing,  between the interval 50-60 speed is decreasing, between the interval 60-65 speed is increasing and between the interval 65-73 speed is constant.

In the third curve between the interval 73-85 speed is increasing,  between the interval 85-92 speed is constant and  between the interval 92-100 speed is decreasing.

Therefore, option B is the correct answer.

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Answer:

Therefore, Ashira's finance charge is $50.

Step-by-step explanation:

To calculate Ashira's finance charge, we need to find the total amount she will pay for the game system through the installment plan and subtract the original purchase price.

Total amount paid = Monthly payment * Number of months

Total amount paid = $55 * 6

Total amount paid = $330

Finance charge = Total amount paid - Purchase price

Finance charge = $330 - $280

Finance charge = $50

Therefore, Ashira's finance charge is $50.

Answer:

Step-by-step explanation:

Given  

3 rectangular cards

each card is 8 inches by 9 inches

The way that she can arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter is that:

Put 3 cards together according to the length

So  the smallest possible perimeter is:

8 + 8 + 8 + 8 + 8 + 8 + 9 + 9 = 66 inches as you can see in the attached photo.

The area of the polygon is equal to the combined area of the 3 cards without overlapping or extending.

The second one is the answer just think of symmetry and if its symmetrical or not.

Answer:

The answer is A

Step-by-step explanation:

Odd symmetry is like the opposite of one side

The graph that best represents a quadratic function that has only one zero is Option C.

We are given that;

The four graphs of the function

Now,

A quadratic function has only one zero if its graph intersects the x-axis at only one point. This occurs when the discriminant of the quadratic equation is equal to zero:

b^2 - 4ac = 0

x = (-b ± sqrt(b^2 - 4ac)) / 2a

If the discriminant is equal to zero, then there is only one solution to the quadratic equation, which means that the graph of the quadratic function intersects the x-axis at only one point.

Therefore, by the given graphed function the answer will be Option C.

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The altitude of the triangle is 1/6 units,

To calculate the altitude of the triangle formed by the given lines, we need to find the distance between the base of the triangle and the vertex opposite to it.

First, let's find the coordinates of the vertices of the triangle. We can start by finding the intersection points of the lines forming the sides of the triangle:

Line 1: 3x + 2y - 10 = 0

Line 2: x + 6y - 10 = 0

Solving these two equations simultaneously will give us the coordinates of the vertices.

Solving Line 1 and Line 2:

3x + 2y - 10 = 0

x + 6y - 10 = 0

Multiplying the second equation by 3, we get:

3(x + 6y - 10) = 0

3x + 18y - 30 = 0

Now we have two equations:

3x + 2y - 10 = 0

3x + 18y - 30 = 0

Subtracting the first equation from the second equation:

(3x + 18y - 30) - (3x + 2y - 10) = 0

16y - 20 = 0

16y = 20

y = 5/4

Plugging the value of y into the first equation:

3x + 2(5/4) - 10 = 0

3x + 5/2 - 10 = 0

3x - 10/2 = 0

3x - 5 = 0

3x = 5

x = 5/3

So one vertex of the triangle is at (5/3, 5/4).

Now, let's find the equation of the line forming the base of the triangle:

By simplifying the given equation: 6x - 8x + 3 = 0

-2x + 3 = 0

-2x = -3

x = 3/2

So the base line has the equation x = 3/2.

To calculate the altitude, we need to find the perpendicular distance from the vertex (5/3, 5/4) to the base line x = 3/2. The perpendicular distance is the shortest distance between the vertex and the base.

The shortest distance between a point and a line can be found using the formula:

Distance = |Ax + By + C| / sqrt(A^2 + B^2)

For the equation x = 3/2, we can rewrite it as 2x - 3 = 0, which represents the line x - (3/2) = 0.

Comparing this with the general equation Ax + By + C = 0, we have A = 2, B = 0, and C = -3.

Now, substituting the values into the formula for the perpendicular distance:

Distance = |2(5/3) + 0(5/4) - 3| / sqrt(2^2 + 0^2)

Distance = |10/3 - 3| / sqrt(4)

Distance = |10/3 - 9/3| / 2

Distance = |1/3| / 2

Distance = 1/6

Hence, the altitude of the triangle is 1/6.

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The number of doves for 5 eagles is 15 doves.

Given:

2 sparrows = 1 parrot

2 parrots = 3 crows

3 crows = 1 dove

3 doves = 1 eagle

We can start by converting the units to find the value of 1 eagle in terms of sparrows:

2 sparrows = 1 parrot

2 parrots = 3 crows

3 crows = 1 dove

On simplifying the equation , we get

Therefore, we can substitute these values to find the conversion from sparrows to doves:

2 sparrows = 1 parrot = (2 parrots) * (3 crows) = (2 * 3 crows) = 6 crows

1 dove = 3 crows

So, in terms of sparrows:

1 dove = 6 crows = 12 sparrows

On simplifying the equation , we get

3 doves = 1 eagle

Substituting the value we found for 1 dove:

3 doves = 12 sparrows = 1 eagle

Now, we can find the value of 5 eagles:

5 eagles = 5 * (1 eagle) = 5 * (3 doves) = 15 doves

Hence , the number of doves is 15.

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Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Answer:

the value of {f/g}(5) is 10.8.

Step-by-step explanation:

To find the value of {f/g}(5), we need to evaluate the function f(x)/g(x) at x = 5.

First, let's calculate f(5) and g(5):

f(5) = 7 + 4(5) = 7 + 20 = 27

g(5) = (1/2)(5) = 5/2 = 2.5

Now, we can find {f/g}(5) by dividing f(5) by g(5):

{f/g}(5) = f(5) / g(5) = 27 / 2.5 = 10.8

If the function f(x)=7+4x and g(x)=1/2x, the value of {f/g}(5) is 10.8.

To calculate the value of {f/g}(5), substitute x = 5 into the expression for f(x) and g(x) and then divide f(5) by g(5).

Given that:

f(x) = 7 + 4x

g(x) = (1/2)x

f(5) = 7 + 4(5)

= 7 + 20

= 27

So,

g(5) = (1/2)(5)

= 5/2

= 2.5

Hence,

{f/g}(5) = f(5) / g(5)

= 27 / 2.5

= 10.8

Thus, 10.8 is the value of {f/g}(5).

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The rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

To convert polar coordinates (r, θ) to rectangular coordinates (x, y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the given polar coordinates are (3√5, -π/8).

Applying the formulas, we have:

x = (3√5) * cos(-π/8)

y = (3√5) * sin(-π/8)

Evaluating the trigonometric functions using a calculator or trigonometric tables, we find:

x ≈ 3.35

y ≈ -0.77

Rounding these values to the nearest hundredth, the rectangular coordinates of the polar coordinates (3√5, -π/8) are approximately (3.35, -0.77).

Please note that the angle -π/8 represents a counterclockwise rotation of π/8 radians from the positive x-axis in the Cartesian coordinate system.

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Answer:

None of these

Step-by-step explanation:

Step 1:

75 kg x Rs.30 = 2250

25 kg x Rs.36 = 900

Total Cost Price = 2250 + 900 = Rs.3150.

Cost Price per Kg = 3150 / 100 = 31.5

Gain of 10% will be;

31.5 x 10 / 100 = 3.15

Cost Price with gain of 10% will be = 31.5+3.15 = Rs. 34.65.

Answer:

Hence, The correct option is (B), NONE OF THESE

Step-by-step explanation:

Make a plan:

Solve the Problem:

30 per kg is:  

75 * 30 = 2250

The cost price of 25 kg of sugar at Rs

36 per  kg is:

25 * 36 = 900

2250 + 900 = 3150

3150 * 1.1 = 3465

75 + 25 = 100 kg

3465 / 100 = 34.65

Draw the conclusion:

Rs  34.65

Hence, The correct option is (B) NONE OF THESE.

Hope this helps!

All of these are top 3 areas that the federal government spends tax money on EXCEPT: Option B: Education

The three primary sectors where tax money is generally allocated by the federal government are Social Security, Medicaid, and the armed forces.

Nevertheless, education would be the only circumstance that deviates from the aforementioned rule. Although education is crucial for government investment, it is usually not among the primary three fields in regards to federal spending.

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See text below

All of these are top 3 areas that the federal government spends tax money on EXCEPT:

Social Security

Education

Medicaid

Military

Answer:

119 people use Redbox

Step-by-step explanation:

42+57+6+14=119

washer + dryer = 1104

dryer = x

washer = 3x

3x + x = 1104

4x= 1104

x = 276 = dryer

washer = 3x = 3(276)= 828

Answer:

Step-by-step explanation:

4p+4q=1 -------- equation 1 -------*+3

3p+2q=7 --------equation 2 -------* +4

12p+12q=3 ------equation 3

     ( - )

12p +8q=28 -----equation 4

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

        4q = -25

        q= -25/4

        q = -6.25

substitute q = -6.25 into equation 1

4p + 4q = 1

4p + 4( - 6.25 ) = 1

4p - 25 = 1

4p = 25 + 1

4p = 26

p = 26/4

p = 6.5

therefore p = 6.5, q = -6.25

q to 1 deimal place = -6.3

The value of x in the triangle is x=3

In the given triangle a midline passing through the middle iof the triangle makes the triangle in to two triangles.

By midpoint segment theorem

x=1/2(x+3)

Apply distributive property

x=x/2+3/2

Take the variable terms on one side and constant on other side

x-x/2=3/2

x/2=3/2

We get the value of x as three

x=3

Hence, the value of x in the triangle is x=3

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Answer:

6

Step-by-step explanation:

The explanation is attached below.

This means that, on average, the player can expect to lose approximately $0.499 per game in the long run. Therefore, participating in this game would result in a net loss for the player over time.

To find the expected value for this game, we need to calculate the average amount the player can expect to win or lose over the long run.

In this case, there are 1000 possible numbers (000 to 999), and the player bets $1 on a specific number (e.g., 115). If the selected number is drawn, the player wins $500. If any other number is drawn, the player loses the $1 bet.

To calculate the expected value, we need to multiply the probability of each outcome by its corresponding payout and sum them up.

The probability of selecting the specific number is 1/1000 since there is only one winning number out of the 1000 possibilities.

Expected value = (Probability of winning * Amount won) + (Probability of losing * Amount lost)

= (1/1000 * $500) + (999/1000 * -$1)

= $0.50 - $0.999

= -$0.499

The expected value for this game is -$0.499.

This means that, on average, the player can expect to lose approximately $0.499 per game in the long run. Therefore, participating in this game would result in a net loss for the player over time.

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Answer:

1640

Step-by-step explanation:

Are of the square

a = [tex]s^{2}[/tex]

a = [tex]10^{2}[/tex]

a = 100

Area of a trapezoid

a = 1/2(a + b)h

a = 1/2(48 + 40)35

a = 1/2 (48 + 40)35

a = 1/2(88)35

a = 44(35)

a = 1540

100 + 1540 = 1640

Helping in the name of Jesus.

Answer:

The area is 1640 square meters

Step-by-step explanation:

the area of the short block(top right) is

[tex](10)(10) = 100\\[/tex]

Now, the total length of the top side is(of the bottom portion),

38 + 10 = 48

We can divide the bottom portion into a square and triangular part,

for the square part we get the area,

[tex](40)(35)=1400[/tex]

For the triangle, we first have to find the length of the base,

which we see from the figure that it will be,

48 - 40 = 8

(and height is 35)

so the area of the triangle is,

[tex](1/2)(8)(35)=140[/tex]

so the total area of the park is

[tex]140 + 1400 + 100 = 1640[/tex]

Answer:

RQ / SQ

Step-by-step explanation:

We see in the figure that angles O and R are congruent, which is what the ) symbol by the two angles indicates.

We see that the first ratio starts with OQ and ends with PQ to give us OQ/PQ.  Since R and O are congruent, the only ratio that would make the statement true is RQ/SQ.

Answer:

(a) 110

Step-by-step explanation:

We can plug in 7 for a and 3 for b.  Then we can simplify

11(a + b)

11(3 + 7)

11(10)

110

Thus, the value of 11(a + b) when a = 7 and b = 3 is 110, or answer a