Consider the relationship 7r+2t=7. a. Write the relationship as a function r=f(t).
Answer: r = 2/7 -t
Step-by-step explanation: solve r from equation
7r = 2-7t l:7. r = 2/7 - t
The relationship as a function r=f(t) is [tex]\rm f(t)=\dfrac{7-2t}{7}\\\\[/tex].
What is the equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Consider the relationship;
7r+2t=7
Substitute r = f(t) in the equation
[tex]\rm 7r+2t=7\\\\7f(t)+2t=7\\\\ 7f(t)=7-2t\\\\f(t)=\dfrac{7-2t}{7}\\\\[/tex]
Hence, the relationship as a function r=f(t) is [tex]\rm f(t)=\dfrac{7-2t}{7}\\\\[/tex].
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A golf pro wants to determine if Titleist Pro V1 golf balls (1) travel farther, on average, than Callaway Chrome Soft golf balls (2). A robot hits 9 of each ball, selected at random, and the distance traveled is measured. Assume the distances traveled are normally distributed. The average distance traveled by the 9 Titleist Pro V1 golf balls is 261.1 yards with standard deviation 10 yards, and the average distance traveled by the 9 Callaway Chrome Soft golf balls is 249.3 yards with standard deviation 12 yards.
Which test should the golf pro use to determine if Titleist Pro V1 golf balls travel a longer average distance than Callaway Chrome Soft golf balls?
a. pairedt test for means
b. paredz test for means
c. Ottest for proportions
d. test for means
e. test for means
f. Ottest for proportions
Complete options are;
A) Paired t-test for means
B) Paired Z-test for means
C) Z-test for proportion
D) t-test for means
E) Z-test for means
F) t-test for proportion
Answer:
B) Paired Z-test for means
Step-by-step explanation:
We are told that the distances travelled are normally distributed.
We are also trying to find out if the average distance travelled by the Titleist Pro V1 golf balls is farther than that of the Callaway Chrome Soft golf balls.
Also, the standard deviation of both cases are known.
Thus, this is where Paired Z-test for means is used.
According to the desired test, the correct option is:
a. paired t-test for means
At the null hypothesis, it is tested that ball 1 does not travel farther than ball 2, that is, the subtraction is of at most 0:
[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]
At the alternative hypothesis, it is tested if it travels farther, that is:
[tex]H_1: \mu_1 - \mu_2 > 0[/tex]
Since we have the standard deviation for the sample, the t-distribution is used.The values tested are greater than 1, hence, the test is for means.There are two samples, hence a paired test is used.Considering the three bullet points above, the correct option is a.
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(2x-3)/4 + (2x-5)/6= 1/2
Answer:
Step-by-step explanation:
making all terms have a common denominator of 12
(3(2x-3)+2(2x-5))/12=6(1)/12 now the 12s cancel out
3(2x-3)+2(2x-5)=6
6x-9+4x-10=6
10x-19=6
10x=25
x=2.5
A ladder is standing on horizontal ground and rests against a vertical
wall. The ladder is 4.5 m long and its foot is 1.6 m from the wall.
Calculate how far up the wall the ladder will reach. Round your
answer to three decimal places. (Show your working)
Answer:
I don't know how to tell you the answer on this one because you need to know how tall the wall is for this one
Step-by-step explanation:
pleeeaassseee brainliest to first person
Answer:
B. 128
Step-by-step explanation:
Answer:
by using Pythagoras law
hypotenuse ²=perpendicular ²+base²
h²=100²+80²
h²=10000+6400
h=√16400=128.06m
128m is the required answer.
NEED HELP MY GRADE DEPENDS ON THIS QUESTION!!!
Write a congruence statement that describes the figures below.
Answer:
✓ triangle GSP = triangle RKF
Step-by-step explanation:
have a great day!
For each ordered pair, determine whether it is a solution to 7x - 4y= -5.
what is the answer of 17x12
Answer:
204
Step-by-step explanation:
17x12=204
find the ratio of 20 : 50
Answer:
20:50
20/50=40%
Yoko is mailing packages. Each small package costs her $2.20 to send. Each large package costs her $3.40. How much will
it cost her to send 3 small packages and 1 large package?
Answer:
$10
Step-by-step explanation:
3($2.20)+3.40
6.60+3.40=10
Find the
area of each
triangle.
9 m
5 m
8m
Answer:
22.5 [tex]m^{2}[/tex]
Explanation:
The equation for the area of a triangle is [tex]\frac{1}{2}[/tex]bh
In this case, the base is 9 m and the height is 5 m
9x5=45
45/2= 22.5
Salma has ridden 18 miles of a bike course. The course is 20 miles long. What percentage of the course has Salma ridden so far?
Find the inverse of the function, f(x)=5(x-4)^3 +6
trade x and y
Answer:
y=[(x-6)/5]^(1/3)+4
Step-by-step explanation:
f(x)=5(x-4)^3 +6
trade x and y
x=5(y-4)^3 +6
x-6=5(y-4)^3
(x-6)/5=(y-4)^3
[(x-6)/5]^(1/3)=y-4
y=[(x-6)/5]^(1/3)+4
There is an ice cream cake in the freezer. On Monday, the family eats 1/2 of
the cake. On Wednesday, they eat 1/4 of the cake. How much did the family
eat altogether?
Answer: 2/4
Step-by-step explanation: Easy 2 + 2 = 4
Another friend's distance d from you (in feet) after t seconds is given by
d = |80 - 5t|. What does the 80 in the equation represent? What does the 5 in the equation represent? At what times is she 60 ft from you?
말 8.) A baker is ordering eggs for the week. How many cartons of 6 eggs would a baker need to have 225 eggs all together? Explain the reasoning for your answer. (4 pts.)
Answer:
38
Step-by-step explanation:
We know that each carton contains 6 eggs and we need a total of 225. To find this answer, divide 225 by 6, which is 37.5. We would have to round up one because you cannot buy half of a carton. So the answer is 38 cartons.
6. (09.04 LC)
For the equation y = 6x2 – 9x + 22, choose the correct application of the quadratic formula. (5 points)
X
-6+1(6)- 4(-9)(22)
2(-9)
X
6 + (6)- 4-9)(22)
21-9)
--9 +1(-99) - 4(6)(22)
X
2(6)
X
9+(-9) - 4(6)(22)
2(6)
Given:
The quadratic equation is
[tex]y=6x^2-9x+22[/tex]
To find:
The correct application of the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]y=6x^2-9x+22[/tex]
Putting [tex]y=0[/tex], we get
[tex]6x^2-9x+22=0[/tex]
Here, [tex]a=6,b=-9,c=22[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]
The correct application of the quadratic formula is [tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex].
Note: The options are not in proper format.
Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.
What is the perimeter and area?
Answer:
Step-by-step explanation:
If it is a parallelogram the opposite sides will a have the same slope.
Using the diagram we see from the coordinates of A and B:
Slope of AB = (5 - -1)/(-1 - -5)
= 6/4
= 3/2.
In the same way
slope of CD = (2 - -4) / (1 - -3)
= 3/2.
So AB and CD can be shown to be parallel.
Similarly the lines BC and AD are parallel.
So the figure is a parallelogram
Finding the perimeter (counting the units between the points):
Perimeter = 2AB + 2BC
By Pythagoras:
AB = sqrt (6^2 + 4^2) = sqrt 52
BC = sqrt (3^2 + 2^2) = sqrt 13
So Perimeter = 2sqrt52 + 2sqrt13
= 4sqrt13 + 2 sqrt13
= 6sqrt13
or 21.63 unit^2 to 2 decimal places.
Area = sqrt52 * perpendicular distance between the lines AB and CD.
Which is the graph of f(x)= 1 4 (4)^ x ?
Answer:
it is the last graph/D
Step-by-step explanation:
Suzanna uses a 1/4 cup measuring scoop to make her coffee. If she needs to fill her coffee filter with 2 cuos of coffe grounds,how many 1/4 cups scoops will she need to use
Answer:
8
Step-by-step explanation:
1/4 times 8 is 2
A theatre has 46 rows.
There are 42 seats in each row.
During a show at the theatre, there are 50 empty seats.
Work out how many people are watching the show.
Answer:
1882
Step-by-step explanation:
46x42=1932 1932-50=1882
A student received a coupon for 12% off the total purchase price at a clothing store. Let b be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
1. equivalent expression by combining like terms.
b-0.12b
Answer:
the equivalent expression is 0.88(x)
Step-by-step explanation:
Given that
There is 12% off on the total purchase price
Based on the above information
The expression that used the given terms i.e.
b - 0.12b
i.e.
1 - 0.12
= 0.88(x)
Hence, the equivalent expression is 0.88(x)
WILL GIVE BRAINLIEST
Find the area of the shaded region. Round to the tenths place. SHOW YOUR WORK
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Can you plz help right answer plz
Answer:
4.8 inches
Step-by-step explanation:
I NEED HELP ASAP
FIND THE MEASURE OF MISSING ANGLE
Answer:
50
Step-by-step explanation:
a right triangle is = to 180 so you need all angles to add to 180 so you take 180 minus it by 90 and 40 you are left with 50 degrees
If Siny = x Sin (a+y). Prove that
dy/dx=[Sin²(a+y)]/Sina
Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
find the volume of a plastic cube vuilding block with a side length of 12 centimeters
Step-by-step explanation:
Length of the plastic cube (L) = 12 cm
Volume of the cube
= L³
= ( 12)³
= 1728 cm³
Hope it will help :)❤
A bread recipe calls for 1/3 cup of white flour and 5 1/3 cups of whole wheat flour. How much flour do I need in total of my recipe?
Answer:
5 2/3
Step-by-step explanation:
Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n
Answer:
The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.
This means that [tex]p = 0.45[/tex]
Mean and standard deviation for the approximation, for a sample of n:
[tex]\mu = E(X) = np = 0.45n[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]
Calculate the probability that fewer than 320 out of the n
Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]
Just have to replace the value of n, find Z, and then find its pvalue.
Find the circumference and area of the circle. Use 3.14 for π. Round to the nearest hundredth if necessary. r = 2m
The answer is 12.57
But rounded to the nearest tenth is 12.6