Answer:
1472
Step-by-step explanation:
The sum of n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = 19 - 14 = 5 , thus
[tex]S_{23}[/tex] = [tex]\frac{23}{2}[/tex] [ (2 × 9) + (22 × 5) ]
= 11.5 (18 + 110) = 11.5 × 128 = 1472
A theater can seat 160 people . If the theater is 60%full, how many more can fit in the theater
Answer:
64 people can fit in the theater.
Step-by-step explanation:
If 60% is full then calculate how many people is it
[tex] \frac{60}{100} \times 160 = 96 \\ 160 - 96 = 64[/tex]
64 is 40% of 160
So this many people can be accommodated in the theater
Answer:
64 more people can fit in the theater
Step-by-step explanation:
You need to find 60% of 160
10%=16 (divided by 10)
16×6=96
160 (total people)-96(60%)=64
What the the Quotient 7/12 divided by 2/5
Answer:35/24
Step-by-step explanation:
7/12 ➗ 2/5
Next step we change divide sign to multiplication,with the numerator and denominator of the right hand fraction inverted
7/12 x 5/2
(7x5)/(12x2)
35/24
The quotient of 7/12 divided by 2/5 is 35/24.
To divide fractions, you need to multiply the first fraction by the reciprocal (or the multiplicative inverse) of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, to find the quotient of 7/12 divided by 2/5, you multiply 7/12 by the reciprocal of 2/5, which is 5/2.
Here are the steps:
Write down the first fraction: 7/12
Write down the reciprocal of the second fraction: 5/2
Multiply the first fraction by the reciprocal: (7/12) x (5/2)
Multiply the numerators: 7 x 5 = 35
Multiply the denominators: 12 x 2 = 24
Simplify the fraction, if possible: 35/24
Therefore, the quotient of 7/12 divided by 2/5 is 35/24.
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WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
+ At time 0 (beginning), the volume is 5 (feet^3) of sand.
+ After 1 minute, it lefts: 90% of 5 = 0.9*5
+ After 2 minutes, it left 90% of (0.9*5) = 0.9*(0.9*5)
or
[tex]5.(0.9)^{2}[/tex]
+ After 3 minutes, it left 90% of [tex]5.(0.9)^{2}[/tex]
or
[tex]5.(0.9)^{3}[/tex]
.......
+ After x minutes, it left 90% of [tex]5.(0.9)^{x-1}[/tex]
or
[tex]5.(0.9)^{x}[/tex]
So the answer is [tex]5.(0.9)^{x}[/tex], that means C
if f(x)=-x^2 and g(x) = -x^2+4x+5 what is the product
Answer:
[tex]x^{4}[/tex] - 4x³ - 5x²
Step-by-step explanation:
-x²(-x² + 4x + 5) Distribute
[tex]x^{4}[/tex] - 4x³ - 5x²
If this answer is correct, please make me Brainliest!
Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
The function fff is given in three equivalent forms. Which form most quickly reveals the zeros (or "roots") of the function? Choose 1 answer: Choose 1 answer: (Choice A) A f(x)=-3(x-2)^2+27f(x)=−3(x−2) 2 +27f, (, x, ), equals, minus, 3, (, x, minus, 2, ), squared, plus, 27 (Choice B) B f(x)=-3(x+1)(x-5)f(x)=−3(x+1)(x−5)f, (, x, ), equals, minus, 3, (, x, plus, 1, ), (, x, minus, 5, )(Choice C) C f(x)=-3x^2+12x+15f(x)=−3x 2 +12x+15f, (, x, ), equals, minus, 3, x, squared, plus, 12, x, plus, 15 Write one of the zeros. xxx =
Answer:
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
x=5
Step-by-step explanation:
Given the three equivalent forms of f(x):
[tex]f(x)=-3(x-2)^2+27\\f(x)=-3(x+1)(x-5)\\f(x)=-3x^2+12x+15[/tex]
The form which most quickly reveals the zeros (or "roots") of f(x) is
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
This is as a result of the fact that on equating to zero, the roots becomes immediately evident.
[tex]f(x)=-3(x+1)(x-5)=0\\-3\neq 0\\Therefore:\\x+1=0$ or x-5=0\\The zeros are x=-1 or x=5[/tex]
Therefore, one of the zeros, x=5
Answer:
i dont think the one above is correct. here is the correct answer
Step-by-step explanation:
How would you describe the translation from f(x)=x2 to f(x)=x2+5 ?
Answer:
5 units up
Step-by-step explanation:
Adding 5 to the y-value of an (x, y) coordinate moves it up 5 units.
f(x) = x^2 +5 is translated 5 units upward from f(x) = x^2.
Problem 1.) A researcher claims that 96% of college graduates say their college degree has
been a good investment. In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment. At a = 0.05 is there enough evidence to reject the researcher's claim?
Answer:
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
Step-by-step explanation:
Explanation:-
Given data A researcher claims that 96% of college graduates say their college degree has been a good investment.
Population proportion 'P' = 0.96
Q = 1-P = 1- 0.96 = 0.04
In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{1500}{2000} = 0.75[/tex]
Level of significance ∝ = 0.05
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
Test statistic
[tex]Z = \frac{p^{-} - P }{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.75 - 0.96 }{\sqrt{\frac{0.96 X 0.04}{2000} } }[/tex]
[tex]Z = \frac{-0.21}{0.00435} = -52.5[/tex]
|Z| = |-52.5| = 52.5 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
We rejected the researcher's claim
Conclusion:-
A researcher do not claims that 96% of college graduates say their college degree has been a good investment.
A fair coin is flipped 10 times and lands on heads 8 times. Provide a reason to justify the difference between the experimental and theoretical
probabilities. Use the drop-down menus to explain your answer.
There should be a
Choose...
number of trials. With Choose...
flips of the coin, the experimental probability will likely
approach the theoretical probability of Choose...
Answer:
THere will be 8 heads and 2 tails
Step-by-step explanation:
I don't know
The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:
A) 2.5%
B)7 %
C)10%
D) 14%
Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help!
Answer:
x = 8√3y = z = 12√2Step-by-step explanation:
We presume you want the values of x, y, and z.
__
There are two "special triangles" in geometry and trigonometry. They are the 30°-60°-90° right triangle that is half of an equilateral triangle, and the 45°-45°-90° isosceles right triangle that is half a square (cut by the diagonal).
The side ratios of these special triangles are relatively easy to remember. It is useful to memorize them.
__
For the isosceles right triangle, the side lengths are the same. The Pythagorean theorem tells you that if they are both 1, then the hypotenuse is ...
√(1²+1²) = √2
That is, the side lengths of the 45-45-90 triangle are in the ratio ...
1 : 1 : √2
__
For the triangle that is half an equilateral triangle, you know the hypotenuse is twice the length of the shortest side (since we got that short side by cutting a long side in half). Then the longer side can be found from the Pythagorean theorem:
√(2²-1²) = √3
That is, the side lengths of the 30-60-90 triangle are in the ratio ...
1 : √3 : 2
_____
In this problem, we're given the hypotenuse of a 30-60-90 triangle, so we know the short side of it (x) will be half that length:
x = (16√3)/2
x = 8√3
The hypotenuse of the 45-45-90 triangle will be √3 times x, so will be ...
long side of small triangle = (√3)(8√3) = 24
The shorter sides of that 45-45-90 triangle will be this value divided by the square root of 2, so are ...
y = z = 24/√2
We can multiply this by (√2)/(√2) to "rationalize the denominator".
y = z = 12√2
Answer:
8\sqrt{3},\ 12\sqrt{2},\ 12\sqrt{2}
Step-by-step explanation:
The table shows the heights of 40 students in a class.
-Height (h)
in cm-
120 < t < 124
124 < t < 128
128 < t < 132
132 <t< 136
136 <t< 140
__________
-Frequency-
7
8
13
9
3
__________
a) Calculate an estimate for the mean height of the students
Answer:
129.3
Step-by-step explanation:
You have to find the number in the middle of all of the heights and multiply them by the all of the frequency (122x7 etc). When you have those answers, add them together and divide the answer by 40.
Katie runs 3 miles in 28 minutes. At this pace, how long will it take her to run 13.1 miles? Round to the nearest minute.
Answer:
122.6 min
Step-by-step explanation:
3 miles = 28 min
13.1 miles=x
28min x 13.1 miles=366.8/3=122.6 min
Answer:
122mins
Step-by-step explanation:
3 miles take 28mins
Therefore the pace refers to the speed of travel and is 3/28
The new time of travel = distance /speed
= 13.1 / 3/28
=13.1 * 28 /3
=122.27
=122minutes
Solve for the variable 8x + 15 = 63
Answer:
6
Step-by-step explanation:
63-15 =48 48/8 is 6
Answer:
x = 6
Step-by-step explanation:
8x + 15 = 63
8x = 63 - 15
8x = 48
x = 48/8
x = 6
plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
The system of equations y = 2 x minus 1 and y = negative one-fourth x + 3 is shown on the graph below.
On a coordinate plane, 2 lines intersect around (1.8, 2.6).
What is a reasonable estimate for the solution?
(1 and three-fourths, 2 and one-half)
(2 and one-half, 1 and three-fourths)
(1 and one-third, 2 and one-half)
(2 and one-half, 1 and one-third)
Answer:
(1 3/4, 2 1/2)
Step-by-step explanation:
The point of intersection is an "ordered pair." That means the order of the two numbers is important. The first number means something different than the second number.
So, if you want a reasonable estimate for (1.8, 2.6), you need to have the first number in the estimate be close to 1.8. The offered choices are ...
1 3/4 = 1.75
2 1/2 = 2.5
1 1/3 ≈ 1.33
The closest of these to 1.8 is 1.75, so the first choice is the best choice so far.
__
The second number of the estimate needs to be close to 2.6. The offered choices are ...
2 1/2 = 2.5
1 3/4 = 1.75
1 1/3 = 1.33
The closest of these to 2.6 is 2.5, so the first choice is still the best choice.
A reasonable estimate is (1 3/4, 2 1/2).
Answer:
A: (1 3/4, 2 1/2)
Step-by-step explanation:
The fair spinner shown in the diagram above is spun.
Work out the probability of getting a factor of 10.
Give your answer in its simplest form.
Answer:
The answer is "0.2"
Step-by-step explanation:
Given value:
factor = 10
The amount of two divided by the number of options. When both fours and eight gaps are available, that probability can be defined as follows:
[tex]\Rightarrow \frac{2}{10}\\\\\Rightarrow \frac{1}{5}\\\\\Rightarrow 0.2\\[/tex]
Find the first five terms of the geometric sequence defined by a (n)=10
(.1)^n
Answer:
Step-by-step explanation:
a(1) = 10(.1)^1 = 1
a(2) = 10(.1)^2 = 10(0.01) = 0.1
a(3) = 10(.1)^3 = 10(0.001) = 0.01
a(4) = 0.001
a(5) = 0.0001
A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the
function has a negative leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
Mark this and return
Save and Exit
Sabem
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
Help................!.!!.!.!.
Answer:
Step-by-step explanation:
it will be 5 * 14 = 70 cm in real life scale
Answer:
~ 70 cm of the width of the actual item ~
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. Given the information, let us create a proportionality as such:
1 = 14 ⇒ x - width of the actual item
5 x
2. Now let us cross multiply, and solve through simple algebra for x:
14 * 5= x,
x = 70 centimeters of the width of the actual item
If there is a strong correlation between the variables a and b, a may cause b.
True or false?
Answer:
true
Step-by-step explanation:
.
g Suppose a factory production line uses 3 machines, A, B, and C for making bolts. The total output from the line is distributed as follows: A produces 25%, B produces 35%, and C produces 40%. The defect rate for A is 5%, B is 4%, and C is 2%. If a bolt chosen at random is found to be defective, what is the probability that it came from machine A
Answer:
The probability that it came from A, given that is defective is 0.362.
Step-by-step explanation:
Define the events:
A: The element comes from A.
B: The element comes from B.
C: The element comes from C.
D: The elemens is defective.
We are given that P(A) = 0.25, P(B) = 0.35, P(C) = 0.4. Recall that since the element comes from only one of the machines, if an element is defective, it comes either from A, B or C. Using the probability axioms, we can calculate that
[tex]P(D) = P(A\cap D) + P(B\cap D) + P(C\cap D)[/tex]
Recall that given events E,F the conditional probability of E given F is defined as
[tex]P(E|F) = \frac{P(E\cap F)}{P(F)}[/tex], from where we deduce that
[tex]P(E\cap F) = P(E|F)P(F)[/tex].
We are given that given that the element is from A, the probability of being defective is 5%. That is P(D|A) =0.05. Using the previous analysis we get that
[tex] P(D) = P(A)P(D|A)+P(B) P(D|B) + P(C)P(D|C) = 0.05\cdot 0.25+0.04\cdot 0.35+0.02\cdot 0.4 = 0.0345[/tex]
We are told to calculate P(A|D), then using the formulas we have
[tex] P(A|D) = \frac{P(A\cap D)}{P(D)}= \frac{P(D|A)P(A)}{P(D)}= \frac{0.05\cdot 0.25}{0.0345}= 0.36231884[/tex]
Find the area of the shape shown.
Answer:
well area is the space inside of a shape. so you would multiply 2 by 4 because there are 4 sides.
Step-by-step explanation:
Answer: area is 10
Step-by-step explanation:
add top and bottom base
8+2=10
then divide by 2
10/2 = 5
then times 5 by 2
5*2=10
8+2/2 * 2 = 10
10 = area
How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?
Answer:
32?
Step-by-step explanation:
Answer:
Depends on how many spoonfuls of sprinkles per sundae. Is there more details to this question?
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
Find the mean, median, and mode(s) of the data. 4, 6, 5, 4, 4, 5, 4, 8
Please Answer it Quickly :^)
Answer:
[see below]
Step-by-step explanation:
The Mean:Add all values together:
[tex]4+6+5+4+4+5+4+8 = 40[/tex]
There are 8 numbers in the data set.
40 ÷ 8 = 5
The mean of the data is 5.
The Median:Order the numbers in ascending order.
4, 4, 4, 4, 5, 5, 6, 8
There is no exact middle number.
[tex](4+5)/2 =4.5[/tex]
The median of the data is 4.5.
The Mode:'4' appears the most in the data set.
4, 4, 4, 4, 5, 5, 6, 8
The mode of the data is 4.
unga oog boog ogah?
Answer:
ooage booge ohag
Step-by-step explanation:
oomago ooga booga
Answer:
I got a universal translator and got "Hello in caveman goodbye in caveman"
Step-by-step explanation:
Find the mean, median, and mode(s) of the data. Choose the measure that best represents the data. Explain your reasoning. Find the mean, median, and mode(s) of the data with and without the outlier. Which measure did the outlier affect the most? 8, 10, 10, 11, 16, 17, 19, 21, 41
Answer:
Mean: 17
Median: 16
Mode: 10
Step-by-step explanation:
8, 10, 10, 11, 16, 17, 19, 21, 41
Median: (the middle number in the number list/data set) 16
Mode: 10
Mean: 8 + 10 + 10 + 11 + 16 + 17 + 19 + 21 + 41 = 153/9 = 17
The mean is equal to 17. The value of the median is 16 and the value of the mode is 10.
What are mean, mode and median?The mean of the numbers is defined as the ratio of the sum of the total numbers to the total count of the numbers.
The given numbers are,
8, 10, 10, 11, 16, 17, 19, 21, 41
Mean = ( 8 + 10 + 10 + 11 + 16 + 17 + 19 + 21 + 41 ) / 9
Mean = 153/9
Mean = 17
The median is calculated by arranging the numbers in ascending order and the middle term of the data.
8, 10, 10, 11, 16, 17, 19, 21, 41
The median is 16.
The mode is calculated as the highest repetition in the data,
8, 10, 10, 11, 16, 17, 19, 21, 41
Mode: 10
Therefore, the mean is equal to 17. The value of the median is 16 and the value of the mode is 10.
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Which expressions are equivalent to -6.3x - 4.2?
-4.7 - 2.3x + 0.5 - 4x
-5.3x - 4.2 - x
-3.4 - 6.3x - 0.8
-6.2x - 4.2
-4.2x - 6.3
-3.7 - 5.3x + 0.5
multiple choice.
Answer:
(1): -4.7 - 2.3x + 0.5 - 4x
(2):-5.3x-4.2-x
(3):-3.4-6.3x-0.8
Step-by-step explanation:
By Collecting like terms and adding the answer I get -6.3x - 4.2
(1):-4.7-2.3x+0.5-4x
Collect like terms
-2.3x-4x-4.7+0.5
-6.3x-4.2
(2):-5.3x-4.2-x
Collect like terms
-5.3x-x-4.2
-6.3x-4.2
(3): -3.4-6.3x-0.8
Collect like terms
-6.3x-3.4-0.8
-6.3x-4.2
Answer:
The first 3 are equivalent the last 3 aren't.
Step-by-step explanation:
The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per term. A financial administrator at one of the colleges believes that the average cost is higher. The administrator conducted a study using 150 small liberal arts colleges. It showed that the average cost per term is $18,200. The population standard deviation is known to be $1,400. Let α= 0.05. What are the null and alternative hypothesis for this study?
Answer:
The null and alternative hypothesis for this study are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The null hypothesis is rejected (P-value=0.004).
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The significance level is 0.05.
The sample has a size n=150.
The sample mean is M=18200.
The standard deviation of the population is known and has a value of σ=1400.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-2.624)=0.004[/tex]
As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
