Answer :
percentage decrease = {(2.89-2.82)/2.89}x100 = 2.42%
What is a15 of the sequence −7,2,11,…
?
Step-by-step explanation:
a=-7
d=9
n=15
we have to find a15
a(n)= a+(n-1)d
a(15)= -7+(15-1)9
a(15)= -7+126
a(15)=119
so 15 term of the sequence is 119
The 15th term in the given sequence is 119.
The given sequence is −7,2,11,…
Here, a=-7, d=9
What is the formula to find the nth term of the sequence?The formula to find the nth term of the sequence is [tex]a_{n} =a+(n-1)d[/tex].
Now, [tex]a_{15} =-7+(15-1) \times9=119[/tex].
Therefore, the 15th term in the sequence is 119.
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Find the length of MK
The length of the MK is 5 units if the length of MK = length of HK - length of HM.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have a number line shown in the picture.
From the number line:
Length of MK = Length of HK - length of HM
MK = 26 - 21
MK = 5 units
Thus, the length of the MK is 5 units if the length of MK = length of HK - length of HM.
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A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 2 divided by ft for the legs and $ 4 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answer
(4h/√2)+4h
Explanation:
the side length as a function of h will be needed, so we will compute it first,
Let x be the side length of the right isosceles triangle, then using Pythagorean theorem.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
The length of a rectangle is six times its width. The area of the rectangle is 384 square centimeters. Find the dimensions of the rectangle.
Answer:
Width = 8 cm
Length = 48 cm
Step-by-step explanation:
Area of a Rectangle Formula: A = lw
Step 1: Write out expression:
l = 6w
w = w
Step 2: Plug in known variables
384 = 6w(w)
Step 3: Solve for w
385 = 6w²
w² = 64
w = 8
Step 4: Find l
l = 6(8)
l = 48
These figures are similar. The
area of one is given. Find the
area of the other.
area=32 in
9 in
12 in
[ ?
Answer: 18 in²
Step-by-step explanation:
S(fig1)=32 in² . We know that the figures are similar and the correspondonding sides are a1=12 and a2=9
So the coefficient of similarity is k=9/12=3/4
S(fig2)=S(fig1)*k²
S(fig2)=32*(3/4)²=32*9/16=18 in²
The solution is A = 18 inches²
The proportion relation is given by k = 3/4 and the value of A = 18 inches²
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A
Now , the constant of proportionality be k
From the figures , the two figures are similar
Constant of proportionality k = ( side of first figure / side of second figure)
k = 9/12
k = 3/4
Now , the area of the first figure A = 32 ( k )²
On simplifying the equation , we get
A = 32 ( 3/4 )²
A = ( 32 x 9 ) / 16
A = 2 x 9
A = 18 inches²
Therefore , the value of A is 18 inches²
Hence , the proportion is A = 18
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 21 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
(x, y, z) = (45°, 57°, 78°)
Step-by-step explanation:
The problem statement tells you ...
x + y + z = 180
-3x +y +z = 0
0x -y +z = 21
__
Subtracting the second equation from the first gives ...
4x = 180
x = 45 . . . . . . divide by 4
Substituting this into the first equation and adding the third equation gives ...
(45 +y +z) +(-y +z) = (180) +(21)
2z = 156 . . . . simplify, subtract 45
z = 78 . . . . . . divide by 2
y = z -21 = 57
The angle measures are ...
(x, y, z) = (45°, 57°, 78°)
Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation .
Answer:
Step-by-step explanation:
The z-score corresponding to a given area of a distribution, is the number of standard deviations that the values in that area have/are from the mean.
In this case, we have a STANDARD normal distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
The Z-score corresponding to a given area, say the 30th percentile is
X = 0 + (-0.524)(1)
Hence, the X (number of values in the given percentile - in this case, 30th) is same as the z-table or z-calculator value for the 30th percentile in ANY normal distribution.
16 square meters is equivalent to how many square yards?
Answer:
16 square meters is equivalent to 19.14 square yards
Hope this helps you
what is 9 - 4 1/2 ? i need help with that
Answer:
9 - 4 1/2 = 4 1/2.
To calculate this you can do (9 - 4 - 1) + (1 - 1/2).
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▹ Answer
4 1/2 or 4.5
▹ Step-by-Step Explanation
[tex]9 - 4\frac{1}{2} \\= 9 - \frac{9}{2} \\Common denominator = 2\\\\\frac{18}{2} - \frac{9}{2} \\= \frac{9}{2} \\\\= 4 \frac{1}{2} or 4.5[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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Please help. !!!!! Only if you are good at college algebra
Does this table represent a function? Why or why not?
X
у
2
1
2
3
4
4
4
2
5
5
O A. Yes, because every walue corresponds to exactly one y value.
B. No, because one wwalue corresponds to two different yvalues,
C. Yes, because there are two walues that are the same.
O D. No, because two of the y values are the same,
Answer:
Option B is the right optionNo, because one X value corresponds to two different y- values.
Step-by-step explanation:
Function has only one output for each input.
Hope this helps..
Good luck on your assignment..
g Suppose you wish to perform a hypothesis test for a population mean. Suppose that the population standard deviation is known, the population distribution is Normal, and the sample is small. Would you perform a z-test or t-test?
Answer:
z-test.
Step-by-step explanation:
We want to perform an hypothesis test for a population mean.
In the case that the standard deviation of the population is known and the population distribution is normal, even if the sample is small, we will use a z-test.
The usual case is to not know the standard deviation of the population, in which case a t-test is adequate instead of a z-test, taking into account the degrees of freedom of the sample.
There are four different answers to the mathematical question: 3 + 2 * 3^2 = ?
This is because the answer is dependent on the order of precedence. Consider the order of precedence and how it affects mathematical calculations. The four answers are below.
• ((3 + 2) * 3)^2 = 225
• (3 + 2) * (3^2) = 45
• 3 + ((2 * 3)^2) = 39
• 3 +( 2 * (3^2)) = 21
Answer:
The order in which you solve the operations will provide different results and to be able to get the right answer you have to be familiar with the order of operations to know the appropiate steps to solve an operation. According to the order of operations in mathematics, exponents are given precedence over addition and multiplication. Because of that, the exponent is the first you have to solve.
3 + 2 * 3^2
3+2*9
Then, mutiplication is given precedence over addition:
3+18
Now, you can solve the addition and the result is: 21
Because of this, the answer is:
• 3 +( 2 * (3^2)) = 21
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
13. (8 points) The graph of the derivative, f'(x), of a function f() is shown.
(a) (2 points) On what intervals is f(x) increasing or decreasing?
(b) (2 points) At what values of x does f(2) have local maximum or minimum?
(c) (2 points) In what interval is f(x) concave upward or downward?
(d) (2 points) What are the x-coordinates of the inflection points of f(x)?
Which point is on the graph of f(x)=3.4x
Answer: The answer is (1, 12).
12 = 3 x 4^{1}
Step-by-step explanation: Hope it helps!
Answer:
Hi! The answer to your question is (1,12)
Step-by-step explanation:
The steps are:
I attached a picture to make sure if that’s the same problem as yours.
So in the picture you can see that there is option A, B, C, D
When we do A and B we will know that it is wrong
When we try C let’s see what we get!
When I did C I got 3.4₁ which equals to 12
Work:
Y=F [1] which equals to 3.4
3.4=12
So the answer will be C. (1,12)
Hope this helps! :)
Stats A simple random sample of FICO scores is listed below. The mean FICO score is reported to be 678. Assuming that the standard deviation of all FICO scores is known to be 58.3, use a 0.01 significance level to test the claim that these sample FICO scores come from a population with a mean equal to 678. DATA: 714, 751, 664, 789, 818 , 779, 698, 836, 753, 834, 693, 802.
Step-by-step explanation:
The sample mean is:
(714+751+664+789+818+779+698+836+753+834+693+802) / 12
≈ 760.9
At 0.01 significance level and 11 degrees of freedom, the critical value is t = 3.106.
The standard error is 58.3 / √12 = 16.8.
The confidence interval is:
760.9 ± 3.106 × 16.8
(708.6, 813.2)
678 is outside of the confidence interval, so we can conclude with 99% confidence that the sample does not come from a population with a mean of 678.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
What is t-test?A t-test is a statistical test used to determine if there is a significant difference between the means of two groups.
It is often used when the sample size is small or when the population standard deviation is unknown.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
First, we need to calculate the t-value using the following formula:
t = (x - μ) / (s / sqrt(n))
We are given that x = 678, μ = 678, s = 58.3, and n = 12. Substituting these values into the formula, we get:
t = (678 - 678) / (58.3 / sqrt(12))
t = 0
Next, we need to find the critical t-value using a t-distribution table or calculator with 11 degrees of freedom (df = n - 1) and a 0.01 significance level. The critical t-value is 3.106.
Since the calculated t-value of 0 is less than the critical t-value of 3.106, we fail to reject the null hypothesis that the sample FICO scores come from a population with a mean equal to 678.
Thus, in other words, there is not enough evidence to support the claim that the sample FICO scores have a different mean than the population mean of 678.
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Unfortunately, the bus broke down at the distance of 50 km continue the story
Answer:
the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...
The graphs below have the same shape. What is the equation of the red
graph?
Step-by-step explanation:
If they have the same shape, the red graph is a translation of the blue, which is given to be y=x^2.
Since the red graph stays on the y axis at two units above the blue (y=x^2) curve, therefore the red curve is given by y=x^2+2.
The equation of the red graph is f(x) = x² + 2.
Option B is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The graphs of f(x) = x² and f(x) = x² + 2 are both quadratic functions, which means they have a parabolic shape.
The graph of f(x) = x^2 is an upward-opening parabola with its vertex at the origin (0,0).
The parabola is symmetric about the y-axis and the x-axis.
The graph of f(x) = x² + 2 is also an upward-opening parabola, but it has been shifted upward by 2 units compared to the graph of f(x) = x².
This means that the vertex of the parabola has been shifted from (0,0) to (0,2).
Thus,
The equation of the red graph is f(x) = x² + 2.
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What percent of the area underneath
this normal curve is shaded?
the answer is not 36%
Answer:
95%
Step-by-step explanation:
Answer:
99.7
Step-by-step explanation:
hope this helps !
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Answer:
t = 5.6 day
t =5 days 14 hours 24 minutes
Step-by-step explanation:
Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.
N = N•e(-kt)
N• = 25
K = 0.1229
Then
N = 25/2 = 12.5
The reason because at the half life , it's original value will decrease to half.
Let's solve for the half life t
N = N•e(-kt)
12.5 = 25e(-0.1229t)
12.5/25 = e(-0.1229t)
0.5 = e(-0.1229t)
In 0.5 =-0.1229t
-0.69314 = -0.1229t
-0.69314/-0.1229 = t
5.6399 = t
To the nearest tenth
5.6 days = t
For a certain salesman, the probability of selling a car today is 0.30. Find the odds in favor of him selling a car today.
Answer:
The odds in favor of him selling a car today are 3 to 10
Step-by-step explanation:
Probability and odds:
Suppose we have a probability p.
The odds are of: 10p to 10
In this question:
Probability of selling a car is 0.3.
10*0.3 = 3
So the odds in favor of him selling a car today are 3 to 10
Karl has $1,500. He spends $375 on a phone and of the rest on a gaming system. What percent of his money is spent on the gaming system?
Answer:
75 %
Step-by-step explanation:
1500 - 375 =1125
So 1125 is spent on the gaming system
Take this over the total amount to get the decimal form
1125/1500 =.75
Change to percent form
75 %
Answer:
75%
Step-by-step explanation:
First we have to find the amount he is using for the gaming system which is
$1500 - $375 = $1125
Now we will express $1125 as a percentage of the total amount and we do that like this;
[tex]\frac{1125}{1500}[/tex] * 100%
= [tex]\frac{1125}{15}[/tex]
=75%
Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y greater-than-or-equal-to 0 and z greater-than-or-equal-to 1 2 x squared z squared StartRoot 8 y cubed z EndRoot 4 x squared y z cubed StartRoot 2 x squared EndRoot 8 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot 64 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot
Answer:
Option C.
Step-by-step explanation:
The given expression is
[tex]\sqrt{128x^8y^3z^9}[/tex]
It can be written as
[tex]\sqrt{(64\cdot 2)\cdot x^8\cdot y^{2+1}\cdot z^{8+1}}[/tex]
[tex]=\sqrt{8^2\cdot 2\cdot (x^4)^2\cdot y^{2}\cdot y\cdot (z^{4})^2\cdot z}[/tex]
[tex]=\sqrt{(8x^4yz^4)^2\cdot 2yz}[/tex]
[tex]=8x^4yz^4\sqrt{2yz}[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
Use the equation Y = 3/27x - 54 +5.
Which is an equivalent equation of the form
y=aVx-h+k
y=-273x +2 +5
y=-3x + 2 + 5
y=33x-2+5
y=27*X-2 +5
Answer:
In the picture below for both parts
Step-by-step explanation:
Edge 2021
The solution is Option C.
The value of the equation is y = 3∛ ( x - 2 ) + 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y = ∛ ( 27x - 54 ) + 5 be equation (1)
On simplifying the equation , we get
y = ∛27 ( x - 2 ) + 5
The cube root of 27 is ∛27 = 3
So , the equation will be
y = 3∛ ( x - 2 ) + 5
Therefore , the value of y is 3∛ ( x - 2 ) + 5
Hence , the equation is y = 3∛ ( x - 2 ) + 5
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Select the correct answer. What is the justification for step 3 in the solution process?
Answer:
Answer B
Step-by-step explanation:
Since you're dividing -0.3 by -2.5, you are using the division property of equality.
Answer:
The division property of equality.
Step-by-step explanation:
I did the test and I got it correct. Hope this helps. :D
I just wish to double check!!
What is the simplified value of the expression below? -8 x (- 3)
A –24
B –11
C 11
D 24
Answer:
24
Step-by-step explanation:
=> (-8)(-3)
So, Here is the rule for it => ( - )( - ) = ( + )
=> +24
Can someone divide this using long division please :)
(4x^3– 2x^2 – 3) divide by (2x^2 - 1)
Answer:
The quotient is 2x+1. The remainder is 2x-2
Step-by-step explanation:
The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.
Answer:
We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Step-by-step explanation:
We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.
Let [tex]\mu[/tex] = population mean score
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5 {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5 {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2
s = sample standard deviation = 4.2
n = sample of students = 40
So, the test statistics = [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex] ~ [tex]t_3_9[/tex]
= 4.066
The value of t-test statistics is 4.066.
Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
The number of liver transplants performed in a particular country in year x is approximated by f (x )equalsnegative 239.7 plus 2390 ln x where x greater than or equals 5 and xequals5 corresponds to the year 1995. a) Estimate the number of transplants in 2013. b) Find f prime (23 ).
Answer:
a) 7265b) 103.913Step-by-step explanation:
Given the number of liver transplants performed in a particular country in year x approximated by f (x) = -239.7+ 2390lnx where x≥5. If x = 5 corresponds to year 1995. x will be equivalent to 23 in the year 2013.
a) Number of transplant in 2013 can be gotten by substituting x = 18 into the equation above.
f (x) = -239.7+ 2390lnx
f (23) = -239.7+ 2390ln 23
f (23) = -239.7+ 2390(3.14)
f(23) = 7264.9
The number of liver transplant in 2013 is approximately 7265
b) If f (x) = -239.7+ 2390lnx
f'(x) = 2390 * 1/x
f'(23) = 2390/23
f'(23) = 103.913