15. Pat and Camilla are working with expressions with rational exponents. Listed below are what each
believes to be correct. Use the properties of exponents to determine the correct answer. Write
the correct answer in the space provided.
Answer:
Step-by-step explanation:
Pat believes that [tex]\sqrt{2}+\sqrt{8}=(2)(2)^{\frac{1}{2}}[/tex]
[tex]\sqrt{2}+\sqrt{8}=\sqrt{2}+\sqrt{4\times 2}[/tex]
[tex]=\sqrt{2}+2\sqrt{2}[/tex]
[tex]=3\sqrt{2}[/tex]
[tex]=3(2)^{\frac{1}{2} }[/tex]
But [tex]2(2)^{\frac{1}{2}}\neq 3(2)^{\frac{1}{2}}[/tex]
Therefore, Pat's belief is not correct.
Camilla believes that [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex]
Which is correct as we have calculated above.
Therefore, [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex] will be the correct answer.
2 (-4x + 2)
What does this equal
Answer:
-8x+4
Step-by-step explanation:
Answer:
-8x+4
Step-by-step explanation:
Andrew brings juice for lunch every 5 days and Hannah brings juice every 7 days they both brought juice today . How many day will it be before they both bring juice ?
Answer:
35 days
Step-by-step explanation:
Andrew brings juice for lunch every 5 days and Hannah brings juice every 7 days
Find the lowest common multiple of 5 and 7
Andrew (every 5 days) = 10, 15, 20, 25, 30, 35, 40, 45, 50
Hannah (every 7 days) = 14, 21, 28, 35, 42, 49, 56
The lowest common multiple of 5 and 7 is 35
Therefore, if Andrew and Hannah both brought juice today, it will take 35 days before they will both bring food again on the same day.
Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co-workers. Sam buys a case of water than contains 36 bottles and sells three times as they bottles as Sylvia sold to his co-workers. How many bottles of water did Sylvia sell if they ended up with the same number of bottles of water left over?
Answer: a
Step-by-step explanation:
Solve this equation, and show work. worth 40 points.
Answer:
[tex]b=-3[/tex]
Step-by-step explanation:
We have:
[tex]25^b\cdot 125^{b+2}=125^b[/tex]
Notice that 125 is the same as 5³. So:
[tex]25^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]
Also, 25 is the same as 5². So:
[tex]((5)^2)^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]
Power of a power property:
[tex]5^{2b}\cdot 5^{3(b+2)}=5^{3b}[/tex]
Power of a product property:
[tex]5^{2b+3(b+2)}=5^{3b}[/tex]
Since they have the same base, the exponents are equal. So:
[tex]2b+3(b+2)=3b[/tex]
Solve for b. Distribute on the left:
[tex]2b+3b+6=3b[/tex]
Combine like terms on the left:
[tex]5b+6=3b[/tex]
Subtract 5b from both sides:
[tex]6=-2b[/tex]
Divide both sides by -2. So, the value of b is:
[tex]b=-3[/tex]
And we're done!
Which pair of numbers is the greatest common factor 15?
Answer:
The answer is 3 and 5
Step-by-step explanation:
3 and 5 is 15 (correct)
10 and 25 is 250 (not correct)
30 and 60 is 1800 (not correct)
60 and 75 is 450 (not correct)
Expand 2(n+7).
2(n+7) = ?
Answer:
2n+14
Step-by-step explanation:
Doreen Schmidt is a chemist. She needs to prepare 24 of a 8% hydrochloric acid solution. Find the amount of 12% solution and the amount of 6% solution she should mix to get this solution.
Step-by-step explanation:
12x+6(24-x)=7*24
12x+144-6x=168
12x-6x =168-144
6x=24
/6
x=4 ounces 12.00%
20 ounces 6.00%
Please help due Monday
Answer:
1. 43, 45, and 47
2. 50, 52, and 54
3. 47 years old
4. 106 degrees
5. 66 degrees
Step-by-step explanation:
1. Let's assume that the first number in the three consecutive odd numbers is x.
We can write an equation to express this now. [tex]x + (x+2) = (x+4) + 41[/tex].
Combining like terms, we get [tex]2x+2 = x+45[/tex]. Subtracting by (x+2) on each side, we get [tex]x = 43[/tex]. Since the smallest number is 43, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 43, 45, and 47.
2. Let's assume that the first number in the three consecutive even integers is x.
We can write an equation to express this now. [tex]x + (x+2) = (x+4)+48[/tex]
Combining like terms, we get [tex]2x+2 = x+52[/tex]. Subtracting by (x+2) on each side, we get [tex]x = 50[/tex]. Since the smallest number is 50, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 50, 52, and 54
3. We can write his current age in years as x. Next year, his age will be x+1. We know that the sum of his current age and his age next year is 73, so we can write an equation to express this.
[tex]x + (x+1) = 73[/tex]. Therefore, 2x + 1 = 73, or 2x = 72. This means that x = 36, or his current age is 36. In 11 years, his age will be 36 + 11 = 47 years old.
4. [tex](21x+1) + (14x+4) = 180[/tex]. Combining like terms, we get [tex]35x + 5 = 180[/tex] Subtracting by 5 on both sides, we get [tex]35x = 175[/tex] This means that [tex]x = 5[/tex]. Now, we can find the degree measures of both angles and find the larger one. The degree measure of the angle on the left is 21(5) + 1 = 106 degrees, and the degree measure of the angle on the right is 14(5) + 4 = 74 degrees. Therefore, the degree measure of the larger angle is 106 degrees.
5. We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can sum the angles up and equate them to 180 degrees.
(x-24) + (2x-108) + (1/3x+12) = 10/3x - 120 = 180. Adding 120 to both sides, we get 10/3x = 300. Multiplying both sides by 3/10, we get x = 900/10 = 90. Therefore, plugging in x = 90, we get 66 degrees.
Jerome biked 1.2 miles. Then he ran 0.75 mile. How far did Jerome go you brainlyest if answerd by you
Answer:
The answer would be 1.95
Step-by-step explanation:
Use the GCF and distributive property to find the expression that is equivalent of 48+56
g precalc Linda works 30 hours per week between two part-time jobs: When she works as a waitress she receives $11.75 per hour and when she works as a math tutor she received $ 17.5 0 per hour. Since she has only 30 hours each week that she can work, the more hours she spends at one job, the fewer number of hours she can work at the second job. If Linda worked a total of 30 hours last week and she worked 9 of these hours as a waitress, how much money did she make last week working at both jobs
Answer:
She made $105.75 working as a waitress
She made $367.50 working as a maths tutor
Step-by-step explanation:
Linda worked a total of 30 hours last week and she worked 9 of these hours as a waitress.
Hence, the number of hours worked as a maths tutor =
30 - 9
= 21 hours
When she works as a waitress she receives $11.75 per hour
Hence, $11.75 × 9 hours
= $105.75
Hence, she made $105.75 working as a waitress
When she works as a math tutor she received $ 17.50 per hour.
$17.50 × 21 hours
$367.50
Hence, she made $367.50 working as a waitress
Consider the statement “Worldwide, there are more than $2.5 trillion in credit card transactions annually.”
What is the daily average dollar amount of transactions? Round to the nearest hundred million dollars.
Answer:
3 trillion
Step-by-step explanation:
because just do the math bu bl I really dk
2 less than five times a number is equal to -17
Answer:
negative 3
Step-by-step explanation:
which two perfect squares is 33.64 between
Answer:
5 and 6 or 25 and 36
Step-by-step explanation:
A full 17 oz bottle of spring water is leaking half of an ounce a minute into an empty bottle. How long will it take for the two bottles to have the same amount of water
Answer:
8.5 minutes
Step-by-step explanation:
the bottle will have leaked half into the 2nd bottle, meaning the 2nd bottle has half too
It will take 17 minutes for the two bottles to have the same amount of water.
What is unit rate?Something calculated for one is called unit rate.
Given that, A full 17 oz bottle of spring water is leaking half of an ounce a minute into an empty bottle.
To have same amount of water both the bottles will have 17/2 = 8.5 ounces of water in them,
Since, it takes a minute to leak or fill half of an ounce,
Therefore, one ounce will take 2 minutes.
Therefore, 8.5 ounces will take = 8.5×2 = 17
Hence, it will take 17 minutes for the two bottles to have the same amount of water.
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which of these planets is Earth explain your answer
Answer:
The answer is Planet B
Step-by-step explanation:
Earth has one bar and Nasa said Earth tempetaure is 15°C
Which is the equation of the graphed line written in
standard form?
A. Y=c
B. X-1/2y=0
C. X-y=0
D. Y= 1/2x
Answer:
C. x - y = 0
Step-by-step explanation:
Step 1: find the slope (m) and y-intercept (b) of the graphed line.
Using the two points on the line (0, 0) and (2, 2),
Slope = [tex] \frac{rise}{run} = \frac{2 - 0}{2 - 0} = \frac{2}{2} = 1 [/tex]
The y-intercept (b) is the point at which the line intercepts the y-axis. Therefore, the y-intercept (b) = 0
Step 2: Generate an equation for the line in slope-intercept form using b = 0 and m = 1.
Substitute m = 1 and b = 0 into y = mx + b
y = 1(x) + 0
y = x
Step 3: rewrite the equation from slope-intercept form to standard form.
To express I'm standard form, take all terms with coefficient to the left, and leave the constant on the right side of the equation.
y = x
Subtract y from both sides
y - y = x - y
0 = x - y
x - y = 0
9) Find the area of the triangle. *
As we can see it's right angle triangle
so:
[tex]Area \: of \: right \: angled \: triangle=( \frac{1}{2} )×base ×height[/tex]Answer:[tex]area \: of \: tringle= \frac{8 \times 6}{2} [/tex][tex]area \: of \: tringle \: = \frac{48}{2} [/tex][tex]area \: of \: triangle = 24✓[/tex]Please help, I’m very confused
Answer:
1st picture: (0,4)
The lines intersect at point (0,4).
2nd picture: Graph D
2x ≥ y - 1
2x - 5y ≤ 10
Set these inequalities up in standard form.
y ≤ 2x + 1
-5y ≤ 10 - 2x → y ≥ -2 + 2/5x → y ≥ 2/5x - 2
When you divide by a negative number, you switch the inequality sign.
Now you have:
y ≤ 2x + 1
y ≥ 2/5x - 2
Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).
In this case, it is all of them.
Next, you would look at the shaded regions.
The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.
That would mean Graph B or D.
Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.
Answer:
A) (-4, 1)
B) graph C
Step-by-step explanation:
A) The point that is in the doubly-shaded area is the solution. The point at (0, 4) is on the dashed line, so is NOT a solution. See the first attachment.
__
B) Look at the given inequalities. You are looking for two things:
which boundary line applieswhich side of that line is shadedHere, you can identify which line goes with which equation a couple of ways. One way is to look at the x- or y-intercept. To find the x-intercept, set y=0 and solve for x. For the first equation, that gives ...
2x ≥ -1
x ≥ -1/2
The steep line, the one that intersects the top of the graph, is the one that has an x-intercept at x = -1/2. You will also note that the solution x ≥ -1/2 means the shading is to the right of that line. (Only graphs C and D have shading to the right of that line.)
For determining which side of the line is shaded, it is useful to pick a variable term with a positive coefficient. For the second inequality, that is 2x. Considering only that term and the relationship in the inequality, we see that we have 2x ≤. This means values of x that are in the solution set are less than (or equal to) those on the boundary line. In other words, shading is to the left of the line with the shallow slope. This is true only for graphs A and C. We have already eliminated graph A, so the desired graph is C.
See the second attachment for what we're talking about here.
57.72 ÷ 0.74 with the equation.
Answer:
x=77.39
Step-by-step explanation:
57.72/.74
is 77.39189 but round it to 77.39
Zoom in to see the question better. Would really appreciate it if someone helped fast thanks!
Answer:
congruent angles
Step-by-step explanation:
find the least number which must be added to 6412 to make it a perfect square
Answer:
The smallest number you can add to 6412 to make it a perfect square is 149. Which would make 6561, and be the square 81
Step-by-step explanation:
How many 5/16 are in. 1. 9/16
Answer:
The answer is 1.8.
Step-by-step explanation:
Simplify:
1) (3x2y3)2
Answer:
6x²y³ I think n hope it's right
The line segment XY is shown in the picture. Which transformation of line segment XY will produce a line segment X'Y' that is parallel to line segment XY?
A
Reflection over the y-axis.
B
Rotation of 90 degrees about point X.
C
Translation up 7 units.
D
Rotation of 180 degrees about point X.
Answer: C
Step-by-step explanation:
I think of a number, multiply it by three, and add fout I get twenty two.
a) Using the statement above, form an equation.
Use the letter 'X' for the unknown number.
b)
Solve the equation.
Answer:
X times 3 + 4 =22
X=6
Step-by-step explanation:
22-4=18
18/3=6
After taking your Freshman English class, you notice there is quite a difference between the students in the classes related to your Business major and your general education requirements. You believe it comes down to a difference in verbal and math abilities. You are interested in seeing how your English classmates performed on two parts of the SAT. You randomly collect data from 28 students on their Math SAT score (population
1), and randomly select another 25 students and collect data on their Verbal SAT score (population
2). After entering the data into Excel you obtain the following output: t-Test: Two-Sample Assuming Unequal Variances Q=0.05 Math SAT Verbal SAT Mean 668. 7604 701.888 Variance 3826.406 6944.827 Observations 28 25 Hypothesized Mean Difference 0 df 44 t Stat P(T<=t) one-tail t Critical one-tail 1.68 P(T<=t) two-tail t Critical two-tail 2.01 What is the value of the test statistic to test if math and verbal scores differ in the SAT exam?
a. -1.479
b. There is not enough information to answer this question
C. -1.627
d. 30.116
e. 30.116
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The sample size for Math SAT is [tex]n_1 = 28[/tex]
The sample size for Verbal SAT is [tex]n_2 = 25[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\mu_1 - \mu_2}{ \sqrt{\frac{\sigma^2_1 }{n_1} + \frac{\sigma_2^2}{n_2} } }[/tex]
substituting 668. 7604 for [tex] \mu_1[/tex] , 701.888 for [tex] \mu_2[/tex], 3826.406 for [tex] \sigma_1^2[/tex] , 6944.827 for [tex]\sigma_2^2[/tex]
So
[tex]t = \frac{668.7604 - 701.888}{ \sqrt{\frac{3826.406}{28} + \frac{6944.827}{25} } }[/tex]
=> [tex]t = 1.627[/tex]
According to General Social Survey of 2016, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 12.9 and a standard deviation of 4.0. The distribution is skewed slightly to the right. For each sample size below: Describe the mean, standard error, and shape of the sampling distribution of the means for a random sample of: (7 pts) a) 16 residents b) 49 residents c) 121 residents Describe the pattern as n increases
Answer:
a) Mean is 12.9
b) Standard Error
i) n = 16, Standard Error = 1
The shape of the sampling distribution means is not normal
ii) n = 49 , Standard Error = 0.5714285714
The shape of the sampling distribution means is normal
iii) n = 121, Standard Error = 0.3636363636
The shape of the sampling distribution means is normal
c)Describe the pattern as n increases
As the number of random samples(n) increases the value for the standard error decreases
Step-by-step explanation:
Central Limit Theorem states that
if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal.
a) 16 residents
Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√16
= 4/4
= 1
n < 30, hence, The shape of the sampling distribution means is not normal
b) 49 residents
= Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√49
= 4/7
= 0.5714285714
n > 30, hence, The shape of the sampling distribution means is normal
c) 121 residents
Mean = 12.9
Standard Error = Standard Deviation /√n
= 4/√121
= 4/11
= 0.3636363636
n > 30, hence, The shape of the sampling distribution means is normal
Describe the pattern as n increases
As the number of random samples(n) increases the value for the standard error decreases
Graph: f(x) = 0.8|x|
Step 1: Identify the dilation
The parent absolute value function will be
factor of
by a
Answer:
it will be shrunk by a factor of 0.8
Step-by-step explanation:
i just got it right
The parent absolute value function will be contract by factor 0.8.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
We have,
f(x) = 0.8 |x|
We know the 0.8 represent the scale factor which leads to dilation.
As, 0.8 < 1 then it means that the figure is going to be contract or smaller than original figure.
Thus, the Function will be contract by factor 0.8
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