Answers
With f(1), we're being given an x-value of 1.
Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.
f(1) = 1 - 2 = -1
Related Questions
Simplify (2s+5-3s)+4(s-6^2)
Answers
Answer: 3s-139
Step-by-step explanation: (2s+5 - 3s)+4(s-6^2)
Collect like terms and evaluate
(-s+5) +4 (s-36)
Rewrite and remove the parentheses
-S+5 +4s -144
Collect like terms and calculate and you get
3s-149
¿Qué distancia hay entre 5 y 8 en la recta numérica? ¿Como lo supiste? ¿Mediante cuál operación se puede llegar al resultado?
Por favor ayúdenme es para hoy
Answers
Answer:
3cm
Step-by-step explanation:
La distancia es 3 centímetros
2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answers
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
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Solve x^2+8x+22=0 by completing the square.
Answers
Answer: x = √-6 - 4
Step-by-step explanation:
x^2+8x+22=0
(x+4)^2 - 16 + 22 = 0
(x+4)^2 + 6 = 0
(x+4)^2 = -6
√(x+4)^2 = √-6
x = √-6 - 4
√6 = 2.449
Michael owns dogs, hamsters and fish in the ratio 2:3:6
If he has 6 hamsters, how many pets does he have?
Answers
Answer:
11
Step-by-step explanation:
I think you just add the ratios together.
6. Error Analysis Dakota said the third term of the expansion of (2g + 3h) is 36g2h². Explain Dakota's error. Then correct the error.
Answers
The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression
Given data ,
Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.
So , on simplifying the equation , we get
= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²
= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²
= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²
Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.
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Pls solve this somebody....
Answers
=====================================================
Explanation:
When two letters are placed together without any space between them, this implies multiplication.
gf = g times f
So we'll be multiplying the functions g and f.
There are two ways to approach this problem.
----------------------------------------------
Method 1
First we need to find f(4) and g(4)
f(x) = 2x+3
f(4) = 2*4+3
f(4) = 8+3
f(4) = 11
g(x) = 2x^2-1
g(4) = 2(4)^2-1
g(4) = 2(16)-1
g(4) = 32-1
g(4) = 31
Now we multiply the results
gf(4) = g(4)*f(4)
gf(4) = 11*31
gf(4) = 341
----------------------------------------------
Method 2
We'll multiply g(x) with f(x) like so
gf(x) = g(x)*f(x)
gf(x) = (2x^2-1)*(2x+3)
gf(x) = 2x^2*(2x+3) - 1(2x+3) .... distribute
gf(x) = 4x^3+6x^2-2x-3 .... distribute again
Now plug in x = 4
gf(x) = 4x^3+6x^2-2x-3
gf(4) = 4(4)^3+6(4)^2-2(4)-3
gf(4) = 4(64)+6(16)-2(4)-3
gf(4) = 256+96-8-3
gf(4) = 341
We get the same result. Method 1 may be the better method, but it will depend on your preference.
Simplify the expression: 2a(4b + 3a) +2ab
Answers
multiply 2a by 4b which makes 8ab then multiply 2a by 3a which is 6a^2 then add the 2ab to the 8ab which gives you 10ab
Which finally gives you 6a^2 + 10ab
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
The surface area of given figure is 200cm². i. Find height of triangle. ii. Find value of y. 80⁰ 5cm 5cm
Answers
Answer:
the answer is 16 . the explanation is that because if you have. 200 cm y axis it overcomes the x of other 80
Read the following prompt and type your response in the space provided. A comparative dot plot is shown for the points scored in a game by the members of two groups. Comparative dot plot. Number line from 41 to 59 for Group A. There is one dot above 41, two dots above 44, three dots above 45, one dot above 46, four dots above 47, two dots above 48, one dot above 49, and one dot above 50. Number line from 41 to 59 for Group B. There is one dot above 41, four dots above 42, five dots above 43, two dots above 44, one dot above 46, one dot above 47, two dots above 49, and three dots above 50. Compare the measures of spread for the two groups.
Answers
In terms of measures of spread, Group B has a wider IQR than Group A
The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.
For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.
For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.
This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.
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7. Triangle XYZ is the preimage of triangle XYZ Find: a. Length of XZ = (show your work) b. Length of X'Z'= (Show your work) C. Scale factor from XZ to XZ = (Show your work X'Z'=6/4. XZ=3/2
Answers
a) The length of XZ can be calculated by the distance formula.
The coordinates of X are (-2,2) and the coordinates of Z are (0,-1).
The distance is:
\(D=\sqrt[]{(2-(-1)^2+(-2-0)^2}=\sqrt[]{3^2+(-2)^2=\sqrt[]{9+4=\sqrt[]{13}\approx}}3.6\)Length of XZ = square root of 13 (approximately 3.6)
b) The coordinates of X' are (-4,4) and the coordinates of Z' are (0,-2).
The distance between X' and Z' is:
\(D=\sqrt[]{(4-(-2)^2+(-4-0)^2}=\sqrt[]{6^2+(-4)^2=\sqrt[]{36+16=\sqrt[]{52}=\sqrt[]{4\cdot13}}}=2\sqrt[]{13\approx}7.2\)Length of X'Z' = two times the square root of 13 (approximately 7.2)
c) The scale factor can be calculated as the ratio between two segments.
In this case, as we have calculated X'Z' and XZ, we are using them:
\(k=\frac{X\text{'Z'}}{XZ}=\frac{2\sqrt[]{13}}{\sqrt[]{13}}=2\)The scale factor is k=2.
We could have calculated it with the coordinates of one point also.
Find missing side length. RIGHT ANSWERS ONLY
Answers
Answer:
13 cm
Step-by-step explanation:
Adding the 5 cm and 8 cm sides creates a segment with the same length as the unknown side.
A previous survey reported that 53% of respondents increased their portfolio value over the past 3 years. How large should a sample be if the margin of error is .03 for a 91% confidence interval
Answers
Answer:
A sample of 796 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
The margin of error is:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In this question, we have that:
\(\pi = 0.53\)
91% confidence level
So \(\alpha = 0.09\), z is the value of Z that has a pvalue of \(1 - \frac{0.09}{2} = 0.955\), so \(Z = 1.695\).
How large should a sample be if the margin of error is .03 for a 91% confidence interval
We need a sample of n, which is found when \(M = 0.03\). So
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.03 = 1.695\sqrt{\frac{0.53*0.47}{n}}\)
\(0.03\sqrt{n} = 1.695\sqrt{0.53*0.47}\)
\(\sqrt{n} = \frac{1.695\sqrt{0.53*0.47}}{0.03}\)
\((\sqrt{n})^2 = (\frac{1.695\sqrt{0.53*0.47}}{0.03})^{2}\)
\(n = 795.2\)
Rounding up
A sample of 796 is needed.
p(x)= 0.75x +50 solve for x
Answers
HELP DUE ON FRIDAY
Some sewing supplies are stored in a container that is 5 inches tall, 7 inches wide, and 12 inches long a. Label the picture of the box with its dimensions b. What is the volume of the box?
Answers
Please help me! My teacher gave us this and has only taught us about rectangles, not rhombi. My classmates and I are very confused
Answers
Step-by-step explanation:
It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other . Opposite angles are equal and adjacen angles sum to 180 degrees .
Then remember alternate angles are equal and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one
If 4 workers can paint a room in 3 hours, then approximately how long does it take 6 workers to paint the same room? Assume the time needed to paint the room is inversely proportional to the number of workers. a. 12 hours c. 3 hours b. 2 hours d. 4 hours Please select the best answer from the choices provided A B C D
Answers
The time it would take six workers to paint the same room given an inverse proportion is 2 hours.
What is the relationship that depicts an inverse proportion?
The formula used to represent inverse proportion is:
y = k/x
Where
• y = dependent variable
• x = independent variable
• k = constant of proportionality
k = yx
4 x 3 =12
How long would it take to paint the room with 6 workers?12 / 6 = 2 hours
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To pay for a home improvement project that total is $20,000 a homeowner is choosing between two different credit card loans with an interest rate of 7% the first credit card compounds interest quarterly or the second credit card compounded monthly the homeowner plans to pay off the loan in 10 years part a determine the total value of a loan with the quarterly compounded interest Show all work and round your answer to the nearest hundred part B determine the total value of the loan with the monthly compounded interest show all work and round your answer to the nearest hundredth Park see what is the difference between the total interest accrued on each loan explain your answer in complete sentences
Answers
A. The total value of the loan with quarterly compounded interest is $52,400.
B. The total value of the loan with monthly compounded interest is $52,010.04
How did we get the values?Part A: Total value of the loan with the quarterly compounded interest
To find the total value of the loan, we'll use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount (loan + interest)
P = principal amount (initial loan) = $20,000
r = interest rate = 7% = 0.07
n = number of times compounded per year = 4 (quarterly)
t = number of years = 10
Plugging in the values, we get:
A = $20,000 * (1 + 0.07/4)^(4 * 10)
A = $20,000 * (1.0175)^40
A = $20,000 * 2.620075
A = $52,401.51
Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.
Part B: Total value of the loan with the monthly compounded interest
To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:
A = P * (1 + r/n)^(nt)
Where:
n = number of times compounded per year = 12 (monthly)
Plugging in the values, we get:
A = $20,000 * (1 + 0.07/12)^(12 * 10)
A = $20,000 * (1.005833)^120
A = $20,000 * 2.600502
A = $52,010.04
Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04
The difference between the two loans is $52,401.51 - $52,010.04 = $391.47
The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.
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12.simplify the following expression
21q + 5/2(3/2) + 4q -5
Answers
Answer:
i think the answer is 25q - 5 / 4
Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price
Answers
Answer:
The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:
$442 * 0.9 = $397.80
The selling price of the same necklace at the competitor's store after 34% and 14% discount is:
$527 * 0.66 * 0.86 = $247.08
So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:
$397.80 - $247.08 = $150.72
To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:
($150.72 / $442) * 100 = 34.11%
Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.
Step-by-step explanation:
if there are 362 men and 73 women what percentage of women are there
Answers
Answer:
16.78%
Step-by-step explanation:
Total = men+women
= 362+73 = 435
Percentage: 73/435 × 100
= 16.78%
Answer:
20%
Step-by-step explanation:
Use 362 as 100% since it is the output value and use 73 as a x value then put them into the equation 100%/x% = 362/73 then flip the equation x%/100% = 73/362
Write an equation. Let x be the unknown number.
10 is the sum of three and twice a number
Answers
Answer:
10 = 3 + 2x
Step-by-step explanation:
twice the number is 2x
the sum of 2x and 3 is written as 2x + 3
2x + 3 =10
So 3 and twice a number..would add up to 10. Twice a number is like times a number by 2.
So let’s write the equation:
10=3+2x or 3+2x=10
on the world globe, the distance between city A and city B is 6.875 inches. The two cities are actually 4469 miles apart. On the same globe, what would be the distance between cities C and city D, two cities that are actually 4761 miles apart? Use a proportion to solve this problem.
Answers
Answer:
7.32 in (nearest hundredth)
or 7.324 in (nearest thousandth)
Step-by-step explanation:
inches : miles
A : B = C : D
6.875 : 4469 = y : 4761
6.875 / 4469 = y / 4761
y = (6.875 / 4469) x 4761
y = 7.32 in (nearest hundredth)
y = 7.324 in (nearest thousandth)
Answer:
the distance between cities C and D is 7.3242 inches.
given:
city A and city B is 6.875 inches, actually 4469 miles apart. city C and city D is x inches, actually 4761 miles apartsolve similarities:
\(\hookrightarrow \sf \dfrac{6.875}{x} = \dfrac{4469}{4761}\)
\(\hookrightarrow \sf 4469(x) = 6.875*4761\)
\(\sf 4469x = 32731.875\)
\(\hookrightarrow \sf x = \dfrac{32731.875}{4469}\)
\(\hookrightarrow \sf x = 7.3242\)
The radius of Circle A is 4 cm. The radius of Circle B is 4 cm greater than the radius of Circle A. The radius of Circle C is 5 cm greater than the radius of Circle B. The radius of Circle D is 3 cm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
*There are 4 parts*
Answers
Answer:
the area for
a=16pi or 50.26548...
b=64pi or 201.061329...
c= 169pi or 530.929158...
d=100pi or 314.159265
d is 19.7392088... or 6.25pi times greater than a
Step-by-step explanation:
the decimal values are more accurate for the d is greater than circle a
so you start with a=4 in radius then b=a+4, c=b+5, d=c-3
then solve the equation a=4, b=8, c=13, d=10
then you solve for the area using the formula radius squared pi
getting the answers above
as for the second answer you would divide d to a getting the amount of times more above for circle d and circle a
which shows how to find the value of this expression when x-2 and y=5\((3 {x}^{3} {y}^{ - 2)2\)
Answers
Here we have the expression:
\((3x^3y^{-2})^2\)We want to find its value when x = -2 and y = 5. For this, we could replace the value of each variable:
\((3\cdot(-2)^3(5)^{-2})^2\)Remember that:
\(\begin{gathered} (-2)^3=(-2)(-2)(-2)=-8 \\ \\ (5)^{-2}=\frac{1}{5^2}=\frac{1}{25} \end{gathered}\)Replacing these values:
\((3\cdot(-8)(\frac{1}{25}))^2=(-\frac{24}{25})^2=\frac{576}{625}=0.9216\)Which is the same that:
\(\frac{3^2(-2)^6}{5^4}\)So the correct option is A.
need to get this right
Answers
The diameter of the engine cylinder is written in the form
|d - 5| ≤ 0.005
How to select the better expressionTo represent the diameter of an engine cylinder with a tolerance of ±0.005 cm and a desired width of 5 cm, we can use an absolute value inequality.
The absolute value inequality representing the permissible limit of variation can be written as:
|d - 5| ≤ 0.005
where:
d represents the diameter of the engine cylinder.
In this inequality, the absolute value of the difference between the diameter (d) and the desired width (5 cm) must be less than or equal to the given tolerance of ±0.005 cm.
This means that the diameter of the engine cylinder can vary within ±0.005 cm of the desired width of 5 cm.
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in a certain urban area, the relationship between number of students, x in thousands, and the umber of schools, y , has an x-intercept of -4 and a y-intercept of 3. Write an equation for this relationship in standard form
Answers
Answer:
\(\sf -3x+4y=12\)
Step-by-step explanation:
x-intercept is when y = 0 → (-4, 0)
y-intercept is when x = 0 → (0, 3)
\(\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{3-0}{0-(-4)}=\dfrac34\)
Substitute one of the points and the found slope into the point-slope form of a linear equation:
\(\implies \sf y-y_1=m(x-x_1)\)
\(\implies \sf y-0=\dfrac34(x-(-4))\)
\(\implies \sf y=\dfrac34(x+4)\)
\(\implies \sf 4y=3(x+4)\)
\(\implies \sf 4y=3x+12\)
\(\implies \sf -3x+4y=12\)
$1,034,473.45 spell it out
Answers
Answer:
One million, thirty four thousand, four hundred and seventy three dollars and forty five cents.
in ace ace g is the centroid and be 15 find bg and ge
Answers
The lengths of BG = 5 and GE = 10.
Given:
G is the centroid and BE = 15
The centroid point g divides the segment BE in the ratio 2:1,
Centroid :
The point in which the three medians of the triangle intersect is known as the centroid of a triangle.
segment:
In geometry, a line segment is bounded by two distinct points on a line.
GE is twice the length of BE
BG = 1/3 * BE
BG = 1/3 * 15
= 15/3
BG = 5
GE = 2/3 * BE
= 2/3 * 15
= 30/3
GE = 10
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