Jenny and Dan have $330 altogether. Jenny has $60 more than Dan. How much should Jenny take from Dan so that she has twice as much as Dan? ​

As per the concept of arithmetic sequence, there are 259 multiples of three between 10 and 787

To solve this problem, we need to find the first and last multiples of three within the given range and then count how many integers are there in between

Step 1: Find the first multiple of three greater than or equal to 10.

The first multiple of three greater than or equal to 10 is 12.

Step 2: Find the last multiple of three that is less than or equal to 787.

The largest multiple of three less than or equal to 787 can be calculated as follows:

Divide 787 by 3:

787 ÷ 3 ≈ 262.33

The largest multiple of three less than or equal to 787 is:

262 × 3 = 786

Step 3: Count the multiples of three within the range.

Now that we have found the first and last multiples of three within the range, we need to count the number of multiples of three between them, including the endpoints.

The multiples of three between 12 and 786 are:

12, 15, 18, ..., 783, 786.

Step 4: Calculate the total count of multiples.

To calculate the total count, we can use the formula for finding the number of terms in an arithmetic sequence:

Number of terms = (last term - first term) / common difference + 1.

In this case, the first term is 12, the last term is 786, and the common difference (the difference between consecutive terms) is 3.

Number of terms = (786 - 12) / 3 + 1

Number of terms = 774 / 3 + 1

Number of terms = 258 + 1

Number of terms = 259.

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Answer:

the probability is the event is certain to happen

Step-by-step explanation:

Answer:

This event is certain to happen.

The probability is 1.

Step-by-step explanation:

Probability theory aims to explain the chance of an event occurring. In this case, there are 3 yellow balls, 4 blue balls and 8 red balls. The total of balls will be 3 + 4 + 8 = 15

If a random ball is removed, it can be any of three colors. The color that has the most balls will have a higher chance of being chosen from the 15 totals.

Likelihood of drawing a red ball: 8/15

Probability of a yellow ball: 3/15

Blue ball probability: 4/15

The question explains that only one ball will be removed and explains that there are only 3 colors. Therefore, when removing a ball, it will certainly be one of three colors.

This can be confirmed by adding the probability of each ball: 8/15 + 3/15 + 4/15 = 15/15 = 1

Thus, if a primary ball is removed, it will certainly be one of three colors. Moreover we can say that chance of being red is greater than being blue, which is greater than being yellow.

Answer:

V≈2770.88

Step-by-step explanation:

The volume of a cylinder that has a radius of 7 and a height of 18 is 2770.88.

In order to find the answer, you should use the formula πr²h.

R means radius and H means Height.

V=πr2h=π·72·18≈2770.88472

Answer:

V = 882pi units^3

or approximately

2769.48 units^3

Step-by-step explanation:

The column of a cylinder is given by

V = pi * r^2 * h

We know the radius is 7 and the height is 18

V = pi * 7^2 *18

V =pi *49 *18

V =882 pi

If we want an approximate answer, we can approximate pi by 3.14

V = 3.14 * 882

V =2769.48

Answer:

The correct option is C

Step-by-step explanation:

The given expression is:

=y²+7y+12/y²-3y-18

Break the middle term of both the numerator and denominator:

=y²+4y+3y+12/y²-6y+3y-18

Take the common from the expressions:

=y(y+4)+3(y+4)/y(y-6)+3(y-6)

=(y+3)(y+4)/(y+3)(y-6)

The same terms will be cancelled: Then we have,

=(y+4)/(y-6)

Therefore the correct option is C....

Answer:

A iS the answer i got it right on my test

Step-by-step explanation:

Y-4/Y-5

ok i think your answer will be from least to greatest it would be this 3 1/5, 3.1, 3.5, 4.2

Hope i helped let me know if i got it right if not i am very sorry.

The order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2  or 3.1. 3 1/5, 3.5, 4.2.

A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56, 2.6, 34 etc. are the numbers.

We have:

The lengths in centimetres of four line segments are:

3.1, 3.5, 3 1/5, 4.2

We can write 3 whole 1/5 as 16/5 or 3.2

3 1/5  = 3.2

3.1, 3.5, 3.2, 4.2

Order from least to greatest:

3.1, 3.2, 3.5, 4.2   or

3.1. 3 1/5, 3.5, 4.2

Thus, the order of four line segments from least to greatest is 3.1, 3.2, 3.5, 4.2  or 3.1. 3 1/5, 3.5, 4.2.

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x+3&(1)\\4x+y=18&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\4x+(x+3)=18\\\\(4x+x)+3=18\qquad\text{subtract 3 from both sides}\\\\5x=15\qquad\text{divide both sides by 5}\\\\x=3\\\\\text{put the value of x to (1):}\\\\y=3+3\\\\y=6[/tex]

Answer:

A) 32

Step-by-step explanation:

I will assume the function is

f(x) = 32 (1.5)^x

This is in the form

y =a b^x

in which a is the initial value, b is the growth rate, x is the time

a =32, which is the initial population

b= 1.5, which means 1.5-1 = .5. which means it grows at a 50% increase

x = number of  years

Answer:

[tex]m=-\frac{4}{5}[/tex]

Step-by-step explanation:

We can take 2 arbitrary points in the graph and solve for slope using the formula shown below.

Note: we will use the 2 points (2,-3) & (-3,1)

Where x_1 = 2, y _1 = -3  and  x _ 2 = -3 and y _ 2 = 1

The formula:

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

Let's plug the numbers and find the slope:

[tex]m=\frac{1-(-3)}{-3-2}\\m=\frac{4}{-5}\\m=-\frac{4}{5}[/tex]

Hence, thsi is the slope.

Answer:

The answers would be:

1) 1/2

2) 1/10

3) 3/4

Step-by-step explanation:

Percentages are always calculated by multiplying the percentages with 100. Like in this example, 50% means 0.5. This 0.5 was multiplied before by 100 to get this percentage. So to find out the equivalent forms, we would simplify the percentage like:

50%-------> 0.5

10%--------> 0.1

75%--------> 0.75

So

0.5 means 1/2 of the total value

0.1 means 1/10 of the total value

0.75 means 3/4 of the total value.

Answer:

Took Quiz 100%.... 50%= 0.50 and 10%= 0.10 and 75% =0.75

I believe the answer would be 12.4 the first choice.

Answer:

=12.4 units

Step-by-step explanation:

We can use the Pythagoras theorem to find the lengths of EF, FG, and HE

(GF)²=(ΔX)²+(Δy)²

(GF)²=(2--1)²+(4-3)²

=3²+1²

=10

GF=√10=3.16 units

(EF)²=(Δx)²+(Δy)²

=(2--1)²+(6-4)²

=3²+2²

=9+4

=13

EF=√13=3.61 units

(HE)²=(Δx)²+(Δy)²

=(-1--3)²+(6-3)²

=2²+3²

=4+9

=13

HE=√13=3.61 units

GH=(-1--3)=2 units

Perimeter =GF+EF+EH+HG

=3.16+3.61+3.61+2

=12.38 units

=12.4 units to 1 decimal place.

Answer:

16.3 units ( to 1 dec. place )

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(- 1, 3) and (x₂, y₂ ) = B(11, - 8)

AB = [tex]\sqrt{(11+1)^2+(-8-3)^2}[/tex]

     = [tex]\sqrt{12^2+(-11)^2}[/tex]

     = [tex]\sqrt{144+121}[/tex]

     = [tex]\sqrt{265}[/tex] ≈ 16.3 ( to 1 dec. place )

Answer:

Answer:

89

°

to the nearest degree.

Explanation:

The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles:

Each with a base of 3.5 and a hypotenuse of 5.

The side opposite the half of the vertex angle is 3.5, the hypotenuse is 5.  

The sine function can be used to find the angle.

sin

θ

=

o

p

p

h

y

p

sin

θ

=

3.5

5

=

0.7

Use the inverse sin function or a table of trig functions to find the corresponding angle . (Arcsin)

arcsin  

0.7

=

44.4

°

Remember that this is the value of half of the vertex angle so double the value to find the vertex angle.

2

×

44.4

=

88.8

°

rounded off to the nearest whole degree =  

89

°

Answer:

1. B. a=14, b=2

2. D. a=1, b=1.4

Step-by-step explanation:

The exponential growth function can be represented as

[tex]y=a\cdot b^x,[/tex]

where b is the growth factor.

1. When the function has equation

[tex]g(x)=14\cdot 2^x,[/tex]

then

[tex]a=14,\\ \\b=2[/tex]

The initial amount is the value of the function at x=0:

[tex]g(0)=14\cdot 2^0=14\cdot 1=14[/tex]

The growth factor is b=2

2. When the function has equation

[tex]f(t)=1.4^t,[/tex]

then

[tex]a=1,\\ \\b=1.4[/tex]

The initial amount is the value of the function at t=0:

[tex]f(0)=1.4^0=1[/tex]

The growth factor is b=1.4

Answer:

The factors of 2q²-5pq-2q+5p are (2q-5p) (q-1)....

Step-by-step explanation:

The given expression is:

2q²-5pq-2q+5p

Make a pair of first two terms and last two terms:

(2q²-5pq) - (2q-5p)

Now factor out the common factor from each group.

Note that there is no common factor in second group. So we will take 1 as a common factor.

q(2q-5p) -1(2q-5p)

Now factor the polynomial by factoring out the G.C.F, 2q-5p

(2q-5p) (q-1)

Thus the factors of 2q²-5pq-2q+5p are (2q-5p) (q-1)....

Answer:

34.4 cm

Step-by-step explanation:

The scale of the map is 1:500000

This means 1 cm in the map is equivalent to 500000 cm in actual.

So, first we need to convert the distance between the 2 towns in centimeters.

The distance between two towns is 172 km

172 km = 172 x 1000 meters = 172,000 meters

172,000 meters = 172,000 x 100 cm = 17,200,000 cm

500,000 cm in actual on the map = 1 cm

1 cm in actual on the map = [tex]\frac{1}{500000}[/tex] cm

17,200,000 cm in actual on the map will be = [tex]\frac{1}{500000} \times 17200000 = 34.4[/tex] cm

Thus, 172 km actual distance would be represented by 34.4 cm on the map

The distance between two towns on a map, with a scale of 1:500000 is 34.4 cm.

The question asks us to calculate the distance, in centimeters, between two towns on a map given the scale of the map is 1:500000, and the actual distance between the two towns is 172 km. First, we convert the actual distance from kilometers to centimeters by multiplying 172 km by 100,000 (since 1 km = 100,000 cm). This gives us 17,200,000 cm. Then, we use the map's scale to find the map distance. The scale 1:500000 means that 1 cm on the map equals 500000 cm in the real world. Therefore, we divide the real-world distance in centimeters by the scale factor (17,200,000 cm / 500000 = 34.4 cm). Thus, the distance between the two towns on the map is 34.4 cm.

Answer:

The value of the expression is -3.

Step-by-step explanation:

Consider the provided expression.

[tex]-3(-3+2)-6[/tex]

Step 1: Solve the parentheses.

[tex]-3(-1)-6[/tex]

Step 2: Open the parentheses.

[tex]3-6[/tex]

Step 3: Subtract the like terms.

[tex]-3[/tex]

Hence, the value of the expression is -3. The required steps is shown above.

Answer:

I'll be referring to this form: ax^2-bx+c

The 4x^2 is the rate that it goes up. If a is greater than 1, then that means the graph gets narrower from the parent function x^2. You can clearly see that in that graph.

The c is always the y-intercept. In this case, you can see that it's 7. The graph clearly shows 7 as it's y-intercept as well, so that matches well.

Sadly, I do not know how to compare the 8x into this situation without a calculator, but that information should be quite enough to see how that function is in that graph.

Answer:

[tex]x=4.459[/tex]

Step-by-step explanation:

We have the following equation

[tex]2^{(x-1)} =11[/tex]

To solve the function, apply the equation [tex]log_2[/tex] on both sides of the equation

[tex]log_2(2^{(x-1)}) =log_2(11)[/tex]

Remember that

[tex]log_b(b)^x =x[/tex]

So

[tex](x-1) =log_2(11)[/tex]

[tex]x =log_2(11) + 1[/tex]

Finally

[tex]x=4.459[/tex]

Answer:

x = 4.46

Step-by-step explanation:

We are to solve the following expression:

[tex]2^{(x-1)}=11[/tex]

Taking the natural logarithm of both sides of the equation to remove the variable from the exponent. to get:

[tex] ln ( 2 ^ { x - 1 } ) = l n ( 1 1 ) [/tex]

[tex] ( x - 1 ) l n ( 2 ) = l n ( 1 1 ) [/tex]

Applying the distributive property:

[tex]xln(2)-1ln(2)=ln(11)[/tex]

Solving for x to get:

[tex]x=\frac{ln(11)}{ln(2)} +1[/tex]

x = 4.46

Answer:

3/4

Step-by-step explanation:

3/14 ÷ 2⁄7

Copy dot flip

3/14 * 7/2

We rewrite

3/2 * 7/14

Canceling a 7 from 7 and 14

3/2 * 1/2

Multiplying straight across

3*1 =3

2*2=4

3/4

For this case we must solve the following expression:

[tex]\frac {\frac {3} {14}} {\frac {2} {7}} =[/tex]

Applying double C we have:

[tex]\frac {3 * 7} {14 * 2} =\\\frac {21} {28} =[/tex]

for simplify we divide the numerator and denominator by 7, then we have:

[tex]\frac {\frac {21} {7}} {\frac {28} {7}} =\\\frac {3} {4}[/tex]

In decimal form we have to:

[tex]\frac {3} {4} = 0.75[/tex]

Answer:

[tex]\frac {3} {4} = 0.75[/tex]

55% off the regular price means she paid 45% of the regular price. ( 100% - 55% = 45%

Multiply the original price by 45%:

39 x 0.45 = 17.55

She paid $17.55

(If you need to know how much she saved:  39 - 17.55 = $21.45)

Answer:

Ashley bought the item for $17.55

Answer: The answer is D. 10! its correct I checked.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Before a dilation you have the point (x,y).

After a dilation of a scale factor of r you have (r*x,r*y).

Let's look at one pair of corresponding points.

A(-11,7)  and A'(22,-14)

We need to figure out what we can multiply to -11 to get 22.

We need to figure out what we can multiply to 7 to get -14.

Hopefully it is the same number or this isn't a dilation.

So to get from pre-image to image you need to multiply by -2 because -11*-2=22 and 7*-2=-14.

The scale factor is -2.

The dilation is this: (x,y)->(-2x,-2y)

The required scale factor is -2

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Let's consider one pair of corresponding points.

Clearly we need to multiply by -2.

This is applicable for all the points

So, the scale factor is -2.

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Answer:

41.04 meters

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. The initial position is given by A. The tree is denoted as C and the fence post is denoted as B. Since the use of sine rule will complicate the question, it will be easier to solve this question using the cosine rule. Therefore, cosine rule will be used to calculate the length of BC. The cosine rule is:

BC^2 = AB^2 + AC^2 - 2*AB*AC*cos(BAC).

The question specifies that AC = 70 meters, BAC = 25°, and AB = 35 meters. Plugging in the values:

BC^2 = 35^2 + 70^2 - 2(35)(70)*cos(25°).

Simplifying gives:

BC^2 = 1684.091844.

Taking square root on the both sides gives BC = 41.04 meters (rounded to two decimal places).

Therefore, the distance between the point on the tree to the point on the fence post is 41.04 meters!!!

Answer:

(a) Plan B, $4 more

(b) 140, Plan A

Let the number of geese be x.

Then number of goats is 22-x.

A goose has 2 legs, and a goat has 4.

There are a total of 82 legs.

So,

2x + 4(22-x) = 82

2x + 88 - 4x = 82

-2x = -6

x = 3

There are 3 geese and (22-3=) 19 goats.

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The solution to the system of linear equations is (3, 0.5).

To solve the system of linear equations by graphing, we'll plot the two equations on the same set of axes and find the point of intersection, which represents the solution.

The solution is (3, 0.5). Confirming for the first equation: y = -3 - 7 = -10 and for the second equation: 3 + 2(0.5) = 4. The coordinates match both equations.

To determine the average number of pies eaten by each participant in a contest with 9 participants and 46 pies, divide the total pies by the total participants. The result is approximately 5.11 pies per person, indicating they ate very evenly with most having eaten about 5 pies.

The question asks us to find out how many pies each person ate in a pie eating contest with 9 participants and 46 pies consumed. To calculate this, we divide the total number of pies by the number of participants. Here's the calculation:

Divide 46 pies by 9 participants to get the average number of pies per person.

The result is approximately 5.11 pies per person.

Since we can't have a fraction of a pie eaten in a real context, it suggests that participants ate either 5 or 6 pies each, if they are very evenly matched.

Therefore, the best description of how many pies each person ate, assuming they are very evenly matched, would be approximately 5 pies per person, with some participants possibly having eaten 6 pies to account for the total of 46 pies.