Consider the expression [tex]6x^3-864x.[/tex] This expression consists of two terms: [tex]6x^3[/tex] and [tex]-864x.[/tex]
These two terms have common factors 6 and x, because:
[tex]6x^3=6x\cdot x^2;[/tex][tex]-864x=6x\cdot (-144).[/tex]Then
[tex]6x^3-864x=6x(x^2-144).[/tex]
You know that [tex]144=12^2.[/tex] Use the formula for the difference of squares:
[tex]x^2-144=x^2-12^2=(x-12)(x+12).[/tex]
Therefore,
[tex]6x^3-864=6x(x-12)(x+12).[/tex]
Answer: correct choice is C.
Given that z20 = –2 and z50= – 1, which of the following do you know?
1.) The variance is 10.
2.) The standard deviation is 30.
3.) The mean is 80.
4.) The median is 40.
5.) The data point x=20 is 2 standard deviations form the mean
6.) The data point x=50 is 1 standard deviation from the mean
7.) The data point x=45 has a z-valued of 1.5
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.
What is standard deviation?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.
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If 88% of milk is water, what percentage do the other components equal
The correct answer is that the other components equal 12% of the milk.
To solve this problem, one must understand that the total percentage of all components in milk must add up to 100%. Given that 88% of milk is water, the remaining percentage will be the sum of all other components in the milk.
To find the percentage of the other components, subtract the percentage of water from the total percentage:
Total percentage of milk = 100%
Percentage of water in milk = 88%
Percentage of other components = Total percentage of milk - Percentage of water in milk
Percentage of other components = 100% - 88%
Percentage of other components = 12%
Therefore, the other components in the milk make up 12% of the milk.
Complete question:- If 88% of milk is water, what percent do the other components equal?
How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.)?
Answer:
2
Step-by-step explanation:
Factor 20x2 + 25x – 12x – 15 by grouping. 1. Group terms with common factors. 2. Factor the GCF from each group. 3. Write the polynomial as a product of binomials.
Answer:
(5x - 3) • (4x + 5)
Step-by-step explanation:
Gina sells 216 cakes in the ratio small :medium:large 5:7:12. 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. Her total profit id £648.45. Work out the profit for one small cake.
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.
Rhianna has $5.25 in dimes and nickels for a total of 63 coins. how many dimes does she have
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.
A system of linear equations is shown below. 2x + 4y = 10 3x – y = 8 marla is attempting to prove that by replacing 2x + 4y = 10 with a different equation it will sometimes produce a new system of equations with the same solution. marla plans on multiplying 2x + 4y = 10 by 2 and then adding the results to the equation 3x – y = 8 in order to create a new equation. marla claims that the new equation that she will replace 2x + 4y = 10 with is 7x + 7y = 12. is marla correct?
No, Marla is not correct. The correct new equation is 4x + 8y = 20.
Explanation: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.
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 2x + 7; (3, 11)
I'm so bad at math please help!??
What is the median for the set of data?
Ages
Stem Leaves
5 0, 4, 6
6 0, 2, 3, 4, 8, 8, 9
7 0, 2, 3, 4, 4, 4, 8, 9
8 4, 5, 6, 8
5|0 = 50 years old
70
71
72
74
Answer:
71
Step-by-step explanation:
A car travels 200 miles in the same time that a train travels 300 miles. The speed of the train is 20 miles per hour more than the speed of the car. Which equation could be used to determine the speed of the car, r, in miles per hour?
A Ferris Wheel turns at a constant speed.
It takes 4 minutes to turn through a complete circle.
What angle does the Ferris Wheel turn through in 90 seconds?
A) 125 degrees
B) 135 degrees
C) 145 degrees
D) 155 degrees
8) A customer paid 84p for 300g of grapes. Find the price for 1/2kg
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
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].
What is the area of a triangle that has a base of 3 feet and a height of 6 feet?
A: 18 ft^2
B: 18 ft C: 9 ft^ 2 D: 4.5 ft^2
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:
Caleb has an offer from a credit card issuer for 0% APR for the first 30 days and 17.68%
APR afterwards, compounded daily. What effective interest rate is Caleb being offered?
17.61%
19.19%
17.68%
19.33%
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
A probe is traveling to mercury is 4.8 x 10^7 miles away the probe travels at a rate of 6 x 10^4 miles per hour. Using the formula: time = distance / rate determine how long it would take the probe to reach mercury all units are in hours.
A. 0.8
B. 2.88 x 10^4
C. 8 x 10^2
D. 1.2 x 10^3
Please help
Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6.
For this case we must simplify the following expression:
[tex]\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6}[/tex]
Simplifying the numerator, dividing all the terms by 4, we have:
[tex]x ^ 2-8x + 12[/tex]
We factor by looking for two numbers that when added together give -8 and when multiplied by 12. These are: -6 and -2
[tex]-6-2 = -8\\-6 * -2 = 12[/tex]
So, we have to:
[tex]x ^ 2-8x + 12 = (x-6) (x-2)[/tex]
Simplifying the denominator:
We rewrite -17x as -18x + x:
[tex]3x ^ 2-18x + x-6[/tex]
We factor the highest common denominator of each group:
[tex]3x (x-6) +1 (x-6)[/tex]
We factor the polynomial by factoring the highest common denominator (x-6):
[tex](x-6) (3x + 1)[/tex]
So, we have to:
[tex]3x ^ 2-17x-6 = (x-6) (3x + 1)[/tex]
Substituting in the original expression we have:
[tex]\frac {(x-6) (x-2)} {(x-6) (3x + 1)} = \frac {x-2} {3x + 1}[/tex]
ANswer:
[tex]\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6} = \frac {x-2} {3x + 1}[/tex]
A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),
E(4, 3), F(4, 1), and G(–1, 1). What is the image of DEFG?
PLEASE ANSWER
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
D(-1, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] D'(-1 - 1, 3 + 2) = D'(-2, 5)E(4, 3) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] E'(4 - 1, 3 + 2) = E'3, 5)F(4, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] F'(4 - 1, 1 + 2) = F'(3, 3)G(-1, 1) [tex]\underset {\longrightarrow } {T_{-1, 2}}[/tex] G'(-1 - 1, 1 + 2) = G'(-2, 3)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
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What is the area of a trapezoid that has bases of 1feet and 14 inches and a height of 3 inches? A 43.5 in.^2 B 87 in.^2 C 22.9 in.^2 D 3.6 in.^2
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:
Harvey the wonder hamster can run 3 1/6 km in 1/4 hour. Harvey runs at a constant rate. Find his average speed in kilometers per hour
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]
Four int variables, x1, x2, y1, and y2, have been declared and been given values. write an expression whose value is the difference between the larger of x1 and x2 and the smaller of y1 and y2.
To find the difference between the larger of x1 and x2 and the smaller of y1 and y2, you first identify these respective values using max and min functions. Then, simply subtract the smaller value from the larger one.
Explanation:To solve this problem, we first identify the larger value between x1 and x2, and the smaller value between y1 and y2. We can do this by using the 'max' function for the variables x1 and x2 and the 'min' function for y1 and y2. Once we have identified these values, we then compute the difference between the larger of x1 and x2 and the smaller of y1 and y2. This concept is based on comparison operations in mathematics.
Here is how it would look like in a programming context:
int larger = Math.max(x1, x2);
int smaller = Math.min(y1, y2);
int difference = larger - smaller;
where 'difference' is the answer you are looking for.
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The explicit rule for a sequence is
an=48−11n .
What is the recursive rule for the sequence?
an=an−1+37,a1=11
an=an−1−11,a1=37
an=an+1−11,a1=37
an=an−1−37,a1=11
Compute the requested value to hundredths of a percent. Choose the correct answer. You see a used car you wish to buy. The dealer quotes you a price of $1,595. You have a Blue Book quotation of $1,435 for the same model and year. How much greater (%) is the dealer's price from the Blue Book? It is _____%.
Answer:
11.15
Step-by-step explanation:
Bianca planted seeds to grow zinnias, sunflowers, and marigolds. After several weeks, 18 out of 50 zinnia seeds, 12 out of 30 sunflower seeds, and 14 out of 40 marigold seeds grew into plants. Drag the names of the plants in order from the least percentage of plants that grew to the greatest percentage of plants that grew.
David has a credit card with an APR of 13.59% and a 30-day billing cycle. The table below details David’s transactions with that credit card in the month of November. Date Amount ($) Transaction 11/1 1,998.11 Beginning balance 11/5 43.86 Purchase 11/16 225.00 Payment 11/23 61.21 Purchase Between the previous balance method and the daily balance method, which method of calculating David’s November finance charge will result in a greater finance charge, and how much greater will it be?
A garden is in the shape of a square. the area of the garden is 178 square meters. the exact length of a side of the garden is between which two lengths?
Which of the following shows the graph of y = 4x + 3?.
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.
marika is training for a track race She starts by sprinting 100 yards . She gradually increases her distance , adding 4 yards a day for 21 days how far does she sprint on day 21
using an=100+(n-1)4
Answer:
180 yards on day 21
Step-by-step explanation:
just took on A P E X !!
PLEASE HELP!!???!!!?
The experimental probability of a coin landing on heads is 7/12. If the coin landed on tails 30 times, find the number of tosses