The average speed of a car is three times as fast as the average speed of a cyclist. to travel 225 km, the cyclist requires 5 h more than the car. determine the average speeds of the cyclist and the car.

Answer:

The profit for one small cake is £1.31.

Step-by-step explanation:

It is given that that Gina sells 216 cakes in the ratio small:medium:large 5:7:12.

[tex]5+7+12=24[/tex]

Number of small cakes = [tex]216\times \frac{5}{24}=45[/tex]

Number of medium cakes = [tex]216\times \frac{7}{24}=63[/tex]

Number of large cakes = [tex]216\times \frac{12}{24}=108[/tex]

The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake.

Let the profit for one small cake be x. So the profit for one medium and large cake are 2x and 3x respectively.

Her total profit id £648.45.

[tex]45\times x+63\times 2x+108\times 3x=648.45[/tex]

[tex]45x+126x+324x=648.45[/tex]

[tex]496x=648.45[/tex]

Divide both sides 496.

[tex]\frac{496x}{496}=\frac{648.45}{496}[/tex]

[tex]x=1.30735887097[/tex]

[tex]x\approx 1.31[/tex]

Therefore the profit for one small cake is £1.31.

its the first graph

A

To find the graph of the equation y = 4x + 3, plot the y-intercept at (0,3) and use the slope of 4 to plot additional points. Connect these points to form a straight line that slopes upward to the right, reflecting a positive slope.

The student has asked to identify the graph of the equation y = 4x + 3. This is an equation of a straight line where the slope (m) is 4 and the y-intercept (b) is 3. According to the properties of linear equations, for every increase of 1 on the x-axis, the value of y will increase by the slope value, which is 4 in this case. The graph will intersect the y-axis at 3, which is the y-intercept.

To graph this line, you can start by plotting the y-intercept at (0,3) on the graph. Then, use the slope to determine the next point by moving 4 units up for every 1 unit you move to the right. Repeat this process with several values of x to construct a table, for instance, at x=1, y=7, at x=2, y=11, etc. These points are then plotted and connected with a straight line to represent the graph of the equation.

Referring to Figure 12.4, we can see that the line would match figure (a) which shows a line that slopes upward to the right, because our b value (slope) is greater than 0.

The formula of area of triangle is given by

[tex] A= \frac{1}{2} b*h [/tex]

Where b is the base and h is the height .

In the given question, base ,b = 3 feet

Height, h= 6 feet

Substituting the values of b and h in the formula, we will get

[tex] A = \frac{1}{2}*3*6 = 9 ft^2 [/tex]

Correct option is C .

Answer:

9 ft^ 2

Step-by-step explanation:

No, Marla is not correct. The correct new equation is 4x + 8y = 20.

No, Marla is not correct. To create a new equation that represents the same system of equations, we need to perform the same mathematical operation on both sides of the equation. In this case, Marla multiplied the left side of the equation by 2, but not the right side. To maintain equality, we need to multiply both sides of the equation by the same constant. Therefore, the correct new equation would be 4x + 8y = 20.

Solution:- Answer is 19.33%

Annual percentage rate (APR) is the yearly rate for a price which have to pay for borrowing money through credit card.

Here Caleb has an offer from a credit card issue for i=0% APR for the first 30 days.

now, effective interest rate for n= 30 days  

=[tex]r=(1+\frac{i}{n} )^n-1\\\Rightarrow\ r=(1+\frac{0}{30} )^{30}-1\\\Rightarrow\ r=(1+0)^{30}-1=1-1=0[/tex]

After 30 days APR =17.68%=0.1768

n=365-30=335 days

now the effective interest rate for n=335 days

=[tex]r=(1+\frac{i}{n} )^n-1\\\Rightarrow\ r=(1+\frac{0.1789}{335} )^{335}-1\\\Rightarrow\ r=(1+0.000527)^{335}-1=(1.000527)^{335}-1=1.1933-1=0.1933[/tex]

=19.33%

So the effective interest rate for 365 days =0+19.33% =19.33%

So fourth option is correct.

Answer:

17.61%

Step-by-step explanation:

just did it

Answer:

I believe its 5.5

Step-by-step explanation:

After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.

Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:

For Jane's investment:

P = $500

r = 8.25% or 0.0825 (as a decimal)

t = 14 years

Plugging these values into the formula gets us:

[tex]A = 500e^{0.0825*14}[/tex]

Calculating this gives us:

[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]

Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.

Answer:The answer is B !

Step-by-step explanation:

A translation is a rigid translation that changes the location of a figure without a net reflection or rotation

The option that gives the correct image of the preimage DEFG, which is D'(-2, 5), E'(3, 5), F'(3, 3), G'(-2, 3), is; The second diagram

Please find attached a diagram showing the preimage and the image

The reason why the selected option is correct is given as follows

The given translation is T₍₋₁, ₂₎(x, y)

Coordinates of the pre-image are D(-1, 3), E(4, 3), F(4, 1), and G(-1, 1)

Required:

To find the image formed following the translation

Solution:

To translate a preimage given the measure of the translation of the x and y-values, in the form T₍₋₁, ₂₎(x, y), '-1' is added to the x-values, and '2' is added to the y-values, as follows

The coordinates of the vertices of the image are D'(-2, 5), E'(3, 5), F'(3, 3), and G'(-2, 3)

The image of DEFG is the second diagram, D'E'F'G'.

Please find attached the diagram of the image of the preimage DEFG constructed with dashes

Learn more about translation transformation here:

https://brainly.com/question/17139588

Answer:

it is 2;3;5;6

Step-by-step explanation:

Given that z20 = –2 and z 50= –1, which of the following do you know?

The variance is 10.

The standard deviation is 30.

The mean is 80.

The median is 40.

The data point x = 20 is 2 standard deviations from the mean.

The data point x = 50 is 1 standard deviation from the mean.

The data point x = 45 has a z-value of 1.5.

answer2356 on edge

The solution is, it is 2;3;5;6.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

Given that z20 = –2 and z 50= –1, which of the following do you know?

The variance is 10.

The standard deviation is 30.

The mean is 80.

The median is 40.

The data point x = 20 is 2 standard deviations from the mean.

The data point x = 50 is 1 standard deviation from the mean.

The data point x = 45 has a z-value of 1.5.

so, we get,

answer2, 3, 5, 6 on edge.

Learn more about standard deviation here:

brainly.com/question/23907081

#SPJ3

Answer:

The correct option is C.

Step-by-step explanation:

Given information: AB=20.4, BC=17.7 and ∠ B = 99 °.

It two sides and their inclined angle is given then the area of the triangle is

[tex]A=\frac{1}{2}ab\sin C[/tex]

Where, a and b are two sides of a triangle and C is their inclined angle.

The area of given triangle is

[tex]A=\frac{1}{2}\times 20.4\times 17.7 \sin 99^{\circ}[/tex]

[tex]A=178.317253[/tex]

[tex]A\approx 178.3[/tex]

The area of the triangle ABC is 178.3 square units. Therefore the correct option is C.

1. f(x)=x²+10x+16

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

So, Vertex = (-5, -9)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

Now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

2. f(x)=−(x−3)(x+1)

By multiplying the factors, the general form is f(x)= -x²+2x+3.

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

So, Vertex = (1, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

3. f(x)= −x²+4

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

So, Vertex = (0, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

Now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

4. f(x)=2x²+16x+30

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

So, Vertex = (-4, -2)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

Now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

5. y=(x+2)²+4

The general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a>0 parabola is opened upward.

if a<0 parabola is opened downward.

Compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

The graph is attached below.

Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.

Answer:

[tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].

Step-by-step explanation:

We are given a geometric sequence { -16, 4, -1, .... }

i.e. [tex]a_{1} =-16[/tex], [tex]a_{2} =4[/tex], [tex]a_{3} =-1[/tex], ...

We will first find the common ratio 'r'.

Now, [tex]r=\frac{a_{n}}{a_{n-1}}[/tex]

i.e. [tex]r=\frac{a_{2}}{a_{1}}[/tex]

i.e. [tex]r=\frac{4}{-16}[/tex]

i.e. [tex]r=\frac{1}{-4}[/tex]

Similarly, i.e. [tex]r=\frac{a_{3}}{a_{2}}[/tex]

i.e. [tex]r=\frac{-1}{4}[/tex]

So, we get that the common ratio is [tex]r=\frac{-1}{4}[/tex].

Now, the recursive formula for the geometric sequence is given by,

[tex]a_{n} =r \times a_{n-1}[/tex]

i.e. [tex]a_{n} =\frac{-1}{4} \times a_{n-1}[/tex]

i.e. [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].

Hence, the recursive formula for this sequence is [tex]a_{n} =\frac{-a_{n-1}}{4}[/tex].

Answer:

(5x - 3) • (4x + 5)

Step-by-step explanation:

Chris should construct the enclosure with a width of 5 feet and a length of 10 feet, using her 15 feet of fencing material, which will result in a maximum enclosed area of 50 square feet.

Chris wants to construct an enclosed rectangular area for a mulch pile and use her backyard's corner fence effectively, thereby constructing only two sides of the mulch pile enclosure. She has 15 feet of fencing material to use and wants the length of the rectangular enclosure to be twice the width. To find the dimensions that will produce the maximum area, we can set up an equation.

Let x represent the width (in feet) and 2x represent the length (in feet), since the length is twice the width.

Since Chris is using the corner of the yard, she only needs to construct two sides of the fence.

Therefore, the amount of fencing material she will use (perimeter of two sides) is given by the equation x + 2x = 15, which simplifies to 3x = 15.

Solving for x, we find that x = 5 feet. Thus, the width of the enclosure is 5 feet, and the length is twice that, or 10 feet.

The maximum area that Chris can enclose is therefore 5 ft  imes 10 ft = 50 square feet.

Answer:

180 yards on day 21

Step-by-step explanation:

just took on A P E X !!

Answer:

Option A. [tex]43.5\ in^{2}[/tex]  

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=(1/2)(b1+b2)h[/tex]

we have

[tex]b1=1\frac{1}{4}\ ft[/tex]

[tex]b2=14\ in[/tex]

[tex]h=3\ in[/tex]

Convert feet to inches first

Remember that

[tex]1\ ft=12\ in[/tex]

so

[tex]1\frac{1}{4}\ ft=\frac{5}{4}\ ft=12*\frac{5}{4}=15\ in[/tex]

substitute in the formula

[tex]A=(1/2)(15+14)3=43.5\ in^{2}[/tex]  

Answer:

43.5 in^2

Step-by-step explanation:

Answer:

11.15

Step-by-step explanation:

The average speed of an object is computed as follows,

[tex]v=\frac{d}{t}[/tex] , where [tex]d[/tex] is the distance covered in the time interval of interest and  [tex]t[/tex]  is the time taken  to cover the distance.

In this problem, the distance covered is

[tex]d= 3\frac{1}{6} km =\frac{19}{6} km.[/tex] as an equivalent fraction.

The time taken for the journey is

[tex]t=\frac{1}{4} hour.[/tex].

The avarage is speed is then,

[tex]v=\frac{d}{t}[/tex]

[tex]v=\frac{(19/6)km}{(1/4)h} =\frac{19\times 4 km}{6\times 1h} =\frac{38km}{3h} = 12.67km/h.[/tex]

Answer:

The number of dimes she has = 42

Step-by-step explanation:

Rhianna has $5.25 in dimes and nickels for a total of 63 coins.

Let the number of nickels be x and the dimes be y.

Since nickels = 0.05 cent and Dimes = 0.10 cent

Now we will form the equations.

10 y + .05 x = 5.25

5x + 10y = 525

x + 2y = 105 ------(1)

x + y = 63 ----(2)

By subtracting equation 2 from 1.

(x + 2y)-(x + y) = 105 - 63

x + 2y - x - y = 42

y = 42

By putting y = 42 in equation 1

x + 42 = 63

x = 63 - 42 = 21

Therefore

Number of dimes will be 42.

Answer:

2

Step-by-step explanation: