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Answer:
rewrite: 2x^2 +5x +20x +50factored: (x +10)(2x +5)Step-by-step explanation:
I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.
You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.
100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10
The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.
The trinomial can be rewritten using these factors as ...
2x^2 +5x +20x +50
Then it can be factored by grouping consecutive pairs:
(2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)
_____
Additional comment
It doesn't matter which of the factors of the pair you write first. If our rewrite were ...
2x^2 +20x +5x +50
Then the grouping and factoring would be (2x^2 +20x) +(5x +50)
= 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring
A club of 10 people wants to choose an executive board consisting of president, secretary, treasurer, and three other officers. In how many ways can this be done
Answer:
The number of ways = 151200
Step-by-step explanation:
Below is the calculation of the number of ways:
Total number of people = 10
Total number of posts = 6
The number of ways = 10P6
The number of ways = [tex]\frac{10!}{10! - 6!}[/tex]
The number of ways = 10 x 9 x 8 x 7 x 6 x 5
The number of ways = 151200
You are dealt one card from a 52-card deck. Find the probability that you are dealt a king or a red card.
Answer:
7/13
Step-by-step explanation:
Half the deck is red so there are 26 reds.
There are 4 kings but we already counted two of these in the 26.
So there are 26+2 red or king cards total.
The probability of selecting a king or red is 28/52.
This can be reduced by dividing top and bottom by 4: 7/13.
An angle with measure of 71° is bisect at what angle?
Answer:
A
Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.
Can someone help please ??
Answer:
x=40
Step-by-step explanation:
In the picture, it seems that angles BHC, CHD, and DHE form a line, 180 degrees. So to solve, set up an equation:
[tex](2x+5)+55+40=180[/tex]
Take off the parentheses and solve.
Subtract 5, 55 and 40 from both sides, or add them together, then subtract.
5+55+40=100
You get:
[tex]2x=80[/tex]
Divide both sides by 2
You get:
[tex][x=40][/tex]I hope this helps!
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 40 couples. Complete parts (a) through (c) below. a. Find the mean and the standard deviation for the numbers of girls in groups of 40 births. The value of the mean is μ
Cross out three digits in the number 51489704 so that the resulting number is divisible by 45. What number is left?
The factors of 45 are 9 and 5.
A number divisible by 45 needs to be divisible by both 9 and 5.
For a number to be divisible by 9 the sum of the digits must also be divisible by 9 and the number needs to end with either a 0 or a 5 to be divisible by 5.
This means the number needs to end with the 0 so cross out the last number (4)
Now find a sum of 5 remaining numbers divisible by 9.
5 + 1 + 4 + 8 + 0 = 18 which is divisible by 9
Cross out 9,7 and the last number 4 to get the number: 51480
An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 11 students who took the course last semester follow:
# of observation(s) n = 30
# of independent variable(s) = 1
SSR = 1,297 SSE= 920
Required:
Find the F test statistic.
Answer:
[tex]F = 39.47[/tex]
Step-by-step explanation:
Given
[tex]n = 30[/tex] --- observations
[tex]p = 1[/tex] -- variables
[tex]SSR = 1,297[/tex]
[tex]SSE= 920[/tex]
Required
The F statistic
This is calculated using:
[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]
[tex]F = 1297 \div \frac{920}{28}[/tex]
Rewrite as:
[tex]F = 1297 * \frac{28}{920}[/tex]
[tex]F = \frac{1297 *28}{920}[/tex]
[tex]F = \frac{36316}{920}[/tex]
[tex]F = 39.47[/tex]
Allen is looking through his weekly local grocery store newspaper ads he notices that Costco is advertising a pack of 60 eggs for $9.35 Safeway is advertising a dozen eggs for $4.79 and Trader Joe's is advertising a pack of 18 eggs for $6.18 which store is offering the better deal?
Answer:
Costco
Step-by-step explanation:
We find the cost per egg for each of the three stores.
Costco:
$9.35/(60 eggs) = $0.15583/egg
Safeway:
$4.79/(12 eggs) = $0.39917/egg
Trader Joe's:
$6.18/(18 eggs) = $0.34333/egg
The best deal is Costco.
Answer:
Costco
Step-by-step explanation:
[tex]\frac{60}{9.35}: \frac{1}{y}[/tex]
60 × y = 1 × 9.35
60y = 9.35
60y ÷ 60 = 9.35 ÷ 60
[tex]y=\frac{187}{1200}[/tex]
[tex]\frac{12}{4.79}: \frac{1}{y}[/tex]
12 × y = 1 × 4.79
12y = 4.79
12y ÷ 12 = 4.79 ÷ 12
[tex]y=\frac{479}{1200}[/tex]
[tex]\frac{18}{6.18}: \frac{1}{y}[/tex]
18 × y = 1 × 6.18
18y = 6.18
18y ÷ 18 = 6.18 ÷ 18
[tex]y=\frac{103}{300}=\frac{412}{1200}[/tex]
Solve the inequality. |X-15|>9
Answer:
X<6 or X>24
Step-by-step explanation:
The hypotenuse of a 45°, 45°, and 90° triangle is 26 sqrt(2) inches. What is the length of each of the other sides?
(A)13 sqrt(2) inches
(B)13 inches
(C)13 sqrt(3) inches
(D)26 inches
remember the pythagorean theorem:
a² + b² = c²
where c is the hypotenuse.
so:
[tex] {a}^{2} + {b}^{2} = { ( \sqrt{26)}}^{2} [/tex]
the square and the square root cancel each other out, so...
a² + b² = 26
we know that a and b are of equal length given the angles.
so it's
[tex] { \sqrt{13} }^{2} + { \sqrt{13} }^{2} = 26[/tex]
here the squares and square roots also cancel, but to keep the equation from the formula true we need to write them. that makes the difference between optional and B
Option A is correct,
[tex] \sqrt{13} inches[/tex]
Round your number to the nearest hundredth 65 7
A graph has time (years) on the x-axis and height (inches) on the y-axis. A line goes through points (2, 5) and (4, 10).
The graph shows the height of a tree over time. What can you deduce the rate of change to be from 2 years to 4 years ?
2 inch per year
2.5 inches per year
5 inches per year
10 inches per year
Answer:
2.5 inches per year
Step-by-step explanation:
We can deduce the rate of change by obtaining the slope or gradient of thw points given :
Gradient = Rise / Run.
Point A (2, 5) ; point B (4, 10)
x1 = 2 ; y1 = 5 ;x2 = 4 ; y2 = 10
Rise = y2 - y1 = 10 - 5 = 5
Run = x2 - x1 = 4 - 2 = 2
Rate of change = Gradient = 5 /2 = 2.5
Which is 2.5 inches per year
Answer: 2.5
Step-by-step explanation: Took the assignment on edge
Hi, Friends,
please help me solve this problem.
Q. terms of a geometric sequence are found by the formula Tn = ar n-1 If a = 3 and r = 2 , find the 4 terms of the sequence.
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Answer:
3, 6, 12, 24
Step-by-step explanation:
It helps if the formula is properly written.
Tn = a·r^(n-1)
Fill in the given values for a, r, and use n = 1 to 4.
T1 = 3·2^(1-1) = 3
T2 = 3·2^(2-1) = 6
T3 = 3·2^(3 -1) = 12
T4 = 3·2^(4 -1) = 24
__
Additional comment
The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.
3, 6, 12, 24, ...
A coordinate plane with a line passing through the points (0, negative 1, 0) and (4, 0).
What is the equation of the graphed line written in standard form?
x – 4y = 4
x + 4y = 4
y = y equals StartFraction one-fourth EndFraction x minus 1.x – 1
y = –y equals negative StartFraction one-fourth EndFraction x minus 1.x – 1
Answer:
x-4y=4
Step-by-step explanation:
The equation of a straight line is in slope intercept form:
y = mx + b;
where y and x are variables, m is the slope of the line and b is the y intercept.
The standard form of a line is:
Ax + By = C
where A, B and C are constants, x and y are variables
The equation of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\[/tex]
Given that a line passes through the points (0, -1) and (4, 0), the equation of the line is given by:
[tex]y-(-1)=\frac{0-(-1)}{4-0} (x-0)\\\\y+1=\frac{1}{4} x\\\\y=\frac{1}{4} x-1\\\\4y=x-4\\\\x-4y=4[/tex]
Answer:
Step-by-step explanation:
Which graph has a domain of all real numbers?
Think of 5 positive integers that have a mean, median, mode, and range of 6.
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2004?
Answer:
The people dies in 2004 by aids are 413042853.4
Step-by-step explanation:
growth factor = 1.8
People died in 1983 = 1800
Let the people dies in 2004 is P.
Time, t = 2004 - 1983 = 21
So,
[tex]P = 1800 \times (1.8)^{21}\\\\P = 413042853.4[/tex]
) A patient drank 12 ounces of orange juice. How many milliliters did the patient drink?
Answer:
[tex]Drink = 354.882\ mL[/tex]
Step-by-step explanation:
Given
[tex]Drink = 12oz[/tex]
Required
Equivalent in mL
We have:
[tex]1\ oz = 29.5735\ mL[/tex]
So:
[tex]Drink = 12 * 29.5735mL[/tex]
[tex]Drink = 354.882\ mL[/tex]
A football is punted so that its path is described by the function h(t) = -4.9(t - 3.5)2 + 15 where h(t) is the height of the football, in meters at time t, in seconds.
What time in seconds does it take for the football to reach its maximum height? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
You already have this set up to answer your question. This quadratic is in work form, aka vertex form, where the vertex is (3.5, 15). The first coordinate of the vertex is the time it takes to reach its max height, which is the second coordinate of the vertex. So it takes 3.5 seconds to reach a max height of 15 meters.
csc(π/2) =__
a.0
b.-1
c.1
d.undefined
Hi there!
[tex]\large\boxed{C. \text{ } 1}[/tex]
csc (π/2)
π/2 is located at (0, 1)
csc is equal to 1/y, or the reciprocal of the y-value
Therefore:
csc(π/2) = 1/1 = 1. C is the correct answer.
What is the value of x if 2/ 3 - 2 = -4 ?
Answer:
x= -3
Step-by-step explanation:
(2x/3)-2=-4
Add 2 to both sides
2x/3=-2
multiply both sides by 3
2x=-6
divide both sides by 2
x= -3
Answer:
x = -3
Step-by-step explanation:
2x/3 - 2 = -4
Add 2 to both sides.
2x/3 = -2
Multiply both sides by 3/2.
x = -2 * 3/2
x = -3
Consider the function h(x) =StartFraction 1 Over x EndFraction . Which graph shows h(2x) + 4? On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It goes through (0.5, 1), (1, negative 2), and (2, negative 3). Another curve opens down and to the left in quadrant 3. It goes through (negative 4, negative 4.5) and (negative 2, negative 5). On a coordinate plane, a curve opens up and to the right in quadrants 1 and 4. It approaches the y-axis in quadrant 1, and then curves down through (0.5, negative 3) and then approaches y = negative 4. Another curves opens down and to the left in quadrant 3. It approaches y = negative 4 and then curves down through (negative 1, negative 4.5). On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (2, 5) and (3, 4.5). Another curve opens down and to the left in quadrants 2 and 3. It goes through (negative 1, 2) and curves down through (negative 0.5, negative 1). On a coordinate plane, a curve opens up and to the right in quadrant 1. It goes through (1, 4.5) and (4, 4). Another curve opens down and to the left in quadrants 2 and 3. It approaches y = 4 and then curves down and approaches the y-axis in quadrant 3. Mark this and return
Answer:
Graph D
Step-by-step explanation:
correct answer on edge :)
Answer:
D
Step-by-step explanation:
Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1004 adults, 86% said that they have a cell phone. Find the value of the test statistic.
Answer: The value of test statistic = -10.67
Step-by-step explanation:
Test statistic for proportion:
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p= population proportion
n= sample size
[tex]\hat{p}[/tex] = sample proportion
AS per given,
p=0.94, n= 1004, [tex]\hat{p}=0.86[/tex]
[tex]z=\dfrac{0.86-0.94}{\sqrt{\dfrac{0.94(1-0.94)}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{\dfrac{0.0564}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{0.0000561752988048}}\\\\=\dfrac{-0.08}{0.00749501826581}\\\\=-10.673756509\approx-10.67[/tex]
i.e. the value of test statistic = -10.67
Find the area of the region that is enclosed between the curves y = x2 and
y = x + 6.
Integrate:
[tex]\displaystyle\int_{-2}^3((x+6)-x^2)\,\mathrm dx = \int_{-2}^3(6+x-x^2)\,\mathrm dx[/tex]
[tex]=\left(6x+\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{-2}^3[/tex]
[tex]=\left(18+\dfrac92-9\right) - \left(-12+2+\dfrac83\right)[/tex]
[tex]=\boxed{\dfrac{125}6}[/tex]
100 POINTS!!!!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Given answer the questions that follow.
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
Answer:
a. The friend is incorrect.
2(x) is the same as x(2). PEMDAS does not apply to the same order of operation under normal conditions and both are directly proportional functions.
b. The parentheses are the only thing making the functions different. After you simplify from the parentheses, both values have the same priority.
Step-by-step explanation:
The sum of 4 consecutive multiples of 6 is 540. What is the greatest of these numbers?
Answer:
144
Step-by-step explanation:
First: 6x
Second: 6x+6
Third: 6x+12
Fourth: 6x+18
- Since they're multiples of 6
[tex]6x+6x+6+6x+12+6x+18=540[/tex]
[tex]24x+36=540\\[/tex]
Subract 36 from each side give us...
[tex]24x=504\\x=21[/tex]
[tex]21(6)+18=144[/tex]
Hope this helped! Please mark brainliest :)
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
Learn more about the Continuous Compounding here:
https://brainly.com/question/24246899
#SPJ2
On planet Ghaap, two Gheeps are worth three Ghiips, two Ghiips are worth five Ghoops, and three Ghoops are worth two Ghuups. How many Ghuups are seven Gheeps worth?
Answer:
10 Ghuups I believe. I am sorry if this is wrong
help me plz----------------------------
9514 1404 393
Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
If a silver alloy that costs $6.75 an ounce is
going to be mixed with 55 ounces of a silver
alloy that costs $10 an ounce to make a
mixture that costs $8 an ounce, how many
ounces of the $6.75 an ounce alloy must be
used?
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Answer:
88 ounces
Step-by-step explanation:
Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...
6.75x +10(55) = 8(55+x)
110 = 1.25x . . . . . . subtract 440+6.75x
88 = x . . . . . . . . divide by 1.25
88 ounces of $6.75/oz silver must be used.
