Answer:
y = x/6 − 11/6
Step-by-step explanation:
y = 6x + 11
To find the inverse, switch x and y, then solve for y.
x = 6y + 11
x − 11 = 6y
y = x/6 − 11/6
Four different digits from 1 to 9 are required to open a safe.
1. The sum of the digits is 20.
2. The first digit is greater than the third.
3. The second and fourth digits differ by at least 5.
4. Exactly two digits are squares.
5. The first and fourth digits add up to a prime number.
6. The fourth digit is the lowest.
Can you find the four-digit combination?
Answer: 5942
Step-by-step explanation:
Clue 4 states exactly two of the digits = 1, 4, or 9
Clue 1 leaves us with the following combinations:
1, 9, 2, 8
1, 9, 3, 7 eliminate by clue 5
4, 9, 2, 5
1, 4, 7, 8
Clue 5 directs us to the following order for 1,9,2,8
2 __ __ 1 --> 2981 or 2891 eliminate by clue 2
9 __ __ 8 --> 9128 or 9218 eliminate by clue 6
9 __ __ 2 --> 9182 or 9812 eliminate by clue 6
Clue 5 directs us to the following order for 4,9,2,5
5 __ __ 2 --> 5492 or 5942 eliminate 5492 by clue 2
9 __ __ 2 --> 9452 or 9542 eliminate by clue 3
Clue 5 directs us to the following order for 1,4,7,8
4 __ __ 1 --> 4781 or 4871 eliminate by clue 2
The only combination not eliminated is 5-9-4-2, which satisfies all six clues.
1) 5 + 9 + 4 + 2 = 20
2) 5 > 4
3) 9 - 2 > 5
4) 4 & 9 but not 1 are included
5) 5 + 2 = 7, which is a prime number
6) 2 < 5, 9, 4
Evaluate geometric series sigma1^20 4(8/9)^n-1
Answer:
32.5861
Step-by-step explanation:
I interpreted it this way:
20 - stop at n = 20 (inclusive)
1 - start at n = 1
4(8/9)^(n - 1) - geometric expression
please tell ans of attached photo
Answer:
192 m^2.
Step-by-step explanation:
We can split this up into 3 rectangles:
Area of the bottom rectangle = 27 * (9-3)
= 27 * 6 = 162 m^2.
Area of rectangle on the left = (18-6)*2
= 24 m^2
Area of small rectangle on the right = 3*2
= 6 m^2
Total area = 162+24+6
192 m^2.
Find the length of a leg of a right triangle (in inches) if the other leg measures 9 in. and the hypotenuse measures 19 in. Round to the nearest thousandth. __________________ in
Answer:
a = 16.733
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 9^2 = 19^2
a^2 = 19^2 - 9^2
a^2 = 361-81
a^2 =280
Taking the square root of each side
sqrt(a^2) = sqrt(280)
a = 16.73320053
Rounding to the nearest thousandth
a = 16.733
Suppose that you collect data for 15 samples of 30 units each, and find that on average, 2.5 percent of the products are defective. What are the UCL and LCL for this process? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round up negative LCL values to zero. Round your answers to 3 decimal places.)
Answer:
The UCL is [tex]UCL = 0.054[/tex]
The LCL is [tex]LCL \approx 0[/tex]
Step-by-step explanation:
From the question we are told that
The quantity of each sample is n = 30
The average of defective products is [tex]p = 0.025[/tex]
Now the upper control limit [UCL] is mathematically represented as
[tex]UCL = p + 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]UCL = 0.025 + 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]UCL = 0.054[/tex]
The upper control limit (LCL) is mathematically represented as
[tex]LCL = p - 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]LCL = 0.025 - 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]LCL = -0.004[/tex]
[tex]LCL \approx 0[/tex]
How does a perpendicular bisector divide a triangle
Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The lengths of W C and C Y are congruent. Which best explains if quadrilateral WXYZ can be a parallelogram? WXYZ is a parallelogram because diagonal XZ is bisected. WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY. WXYZ is a parallelogram because ZC + CX = ZX. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Answer: The answer is D
Step-by-step explanation:
Edge 2021
The true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
What are quadrilaterals?Quadrilaterals are shapes with four sides
What are parallelograms?Parallelograms are quadrilaterals that have equal and parallel opposite sides
The quadrilateral is given as:
WXYZ
Also, we have:
WC = CY
The given parameters are not enough to determine if the quadrilateral is a parallelogram or not
Hence, the true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Read more about quadrilaterals and parallelograms at:
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The function f(x) = -x2 + 40x - 336 models the daily profit, in dollars, a shop makes for selling donut
combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? Show
the work that leads to the answer. (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? Show
the work that leads to the answer. (5 points)
(10 points)
Answer:
This question should be worth atleast 20 points
Step-by-step explanation:
a. For the vertex, input the funtion into the calculator, and see where the turning piont is, that is the vertex.
b. Solve using this vormula.
x= (-b ±[tex]\sqrt{b^2 - 4ac}[/tex])/2a
you will get two asnwrs, both are correct.
pls help help me pls
Answer:
b
Step-by-step explanation:15 x 5 = 75 and 20 x 4 = 80 making 155 and 15 x 3 = 45 and 20 x 2 = 40 making 85
I AM GIVING + 20 POINTS !!!!! PLEASE ANSWER SOON!!!!! Which is NOT a good reason to perform step 1 in the solution shown? equation: 4x = 88 step 1: 4x/4 = 88/4 step 2: x = 22 a. divide by 4, because 4 is a factor of 88. b. dividing 4x by 4 isolates x on one side of the equation. c. dividing is the inverse of multiplying d. dividing both sides by 4 keeps the equation balanced
Answer:
c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.
evaluate -x+4 when x = -2
Answer:
6Step-by-step explanation:
f(x)=-x+4
f(-2)=-(-2)+4
f(-2)=+2+4
f(-2)=6
Answer:
6
Step-by-step explanation:
-(-2)+4=___
+(+2)+4=6
The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is between 920 and 1730lbs round to four decimal places.
Answer:
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Step-by-step explanation:
Step(i):-
Given mean of the Population = 1100 lbs
Standard deviation of the Population = 300 lbs
Let 'X' be the random variable in Normal distribution
Let x₁ = 920
[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]
Let x₂ = 1730
[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]
Step(ii)
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)
= P(-0.6 ≤Z≤2.1)
= P(Z≤2.1) - P(Z≤-0.6)
= 0.5 + A(2.1) - (0.5 - A(-0.6)
= A(2.1) +A(0.6) (∵A(-0.6) = A(0.6)
= 0.4821 + 0.2257
= 0.7078
Conclusion:-
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Answer:
0.7975
Step-by-step explanation:
Which equation represents the line passing through points A and C on the graph below? On a coordinate plane, point A is at (2, 3), point B is at (negative 2, 1), point C is at (negative 4, negative 3), and point D is at (4, negative 5). y= negative x minus 1 y = negative x + 1 y = x minus 1 y = x + 1
The equation that represents the line that passes through the points A and C is y = x + 1
What is a linear equation?A linear equation is an equation that has a constant rate or slope, and is represented by a straight line
The points are given as:
(x,y) = (2,3) and (-4,-3)
Calculate the slope, m using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{-3 -3}{-4 - 2}[/tex]
Evaluate
m = 1
The equation is then calculated as:
y = m *(x - x1) + y1
So, we have:
y = 1 * (x - 2) + 3
Evaluate
y = x - 2 + 3
This gives
y = x + 1
Hence, the equation that represents the line that passes through the points A and C is y = x + 1
Read more about linear equations at:
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#SPJ2
Answer:
y = x + 1
Step-by-step explanation:
Edge2020
Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5
If yall can help me for Pre-Calc, that would be great.
-Thanks.
If the equation is
[tex]7\sin^2x-14\sin x+2=-5[/tex]
then rewrite the equation as
[tex]7\sin^2x-14\sin x+7=0[/tex]
Divide boths sides by 7:
[tex]\sin^2x-2\sin x+1=0[/tex]
Since [tex]x^2-2x+1=(x-1)^2[/tex], we can factorize this as
[tex](\sin x-1)^2=0[/tex]
Now solve for x :
[tex]\sin x-1=0[/tex]
[tex]\sin x=1[/tex]
[tex]\implies\boxed{x=\dfrac\pi2+2n\pi}[/tex]
where n is any integer.
If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...
Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie? A. I B. II C. III D. IV
Answer:
B. II
Step-by-step explanation:
G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.
G' will lie in quadrant II
Answer:
B. 11
Step-by-step explanation:
The area of this parallelogram is 120 ft2 find the value of h
Answer: 6
Step-by-step explanation:
A=bh plus 120 for A and 20 for B
120=20b
/20 divide by 20 each side
H=6
A car is traveling on Michigan Street towards Ward Street. The car planes to turn right into Ward Street. what is the angle measure of the turn.
Pls help ASAP
if p(A)=0.30,p(B)=0.40and p(AB) =0.20,then p(A/B) is
Answer:
p(A|B) = 2/3Step-by-step explanation:
Given p(A)=0.30,p(B)=0.40and p(A∩B) =0.20,then p(A/B) is expressed as shown:
p(A|B) = p(A∩B)/p(A)
p(A|B) means B is independent and A depends on B.
In your problem P(A)=0.65, P(A∩B) =0.1
Substituting the given values,
p(A|B) = 0.2/0.30
p(A|B) = 2/10 * 10/3
p(A|B) = 2/3
The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flute. There are four fewer tuba players than there are trombone player, but three more members play the French horn than play the trombone. The band director, his assistant and six parent volunteers are also going. How many seats are needed on the bus?
Answer:
76
Step-by-step explanation:
Flute players- 5
Trumpet player- 3 times flute players -15
Trombone players- 8 fewer than trumpet-7
Drummers- 11 more than trombone-18
Clarinet- 2 times flute- 10
Tuba-4 fewer than trombone-3
French horn- 3 more than trombone- 10
Band director- 1
Assistant-1
Volunteers- 6
5+15+7+18+10+3+10+1+1+6=76
c. Find the price of 16 shirts if 5 costs GH¢80
Answer:
16 shirts = GH¢256
Step-by-step explanation:
If 5 shirts cost GH¢80
Let's determine the price of 16 shirts by cross multiplying the values
This method of evaluating answers is one of the essential methods .
It's just Making sure that the values within each side of the wall to symbol crosses each other.
But one shirt = GH¢80/5
one shirt = GH¢16
So
5 shirts= GH¢80
16 shirts = (16 shirts * GH¢80)/5 shirts
16 shirts = GH¢1280/5
16 shirts = GGH256
A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.How much work W is done in pulling half the rope to the top of the building
Answer:
180 fb*lb
45 ft*lb
Step-by-step explanation:
We have that the work is equal to:
W = F * d
but when the force is constant and in this case, it is changing.
therefore it would be:
[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]
Where a = 0 and b = 30.
F (x) = 0.4 * x
Therefore, we replace and we would be left with:
[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]
We integrate and we have:
W = 0.4 / 2 * x ^ 2
W = 0.2 * (x ^ 2) from 0 to 30, we replace:
W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)
W = 180 ft * lb
Now in the second part it is the same, but the integral would be from 0 to 15.
we replace:
W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)
W = 45 ft * lb
Following are the calculation to the given value:
Given:
[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]
To find:
work=?
Solution:
Using formula:
[tex]\to W=fd[/tex]
[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]
[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]
Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".
Learn more:
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Will give brainliest answer
Answer:
Radius = 6.5cm
Diameter = 13cm
Step-by-step explanation:
The diameter is given (13)
Radius is half the diameter (13/2=6.5)
Answer:
Radius = 13 / 2 = 6.5 cmDiameter = 13 cmExplanation
RadiusThe straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.
DiameterThe chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.
Hope this helps...
Good luck on your assignment...
Given
f(x) = 2x2 + 1
and
g(x) = 3x - 5
find the following.
f-g
Answer:
The answer is
2x² - 3x + 6Step-by-step explanation:
f(x) = 2x² + 1
g(x) = 3x - 5
To find f - g(x) subtract g(x) from f(x)
That's
f-g(x) = 2x² + 1 - (3x - 5)
= 2x² + 1 - 3x + 5
= 2x² - 3x + 6
Hope this helps you
I NEED HELP PLEASE THANKS!
Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
Answer:
23.29 lbs
Step-by-step explanation:
The force on Jenny due to gravity can be resolved into components perpendicular to the hillside and down the slope. The down-slope force is ...
(90 lbs)sin(15°) ≈ 23.29 lbs
In order to keep Jenny in position, that force must be balanced by an up-slope force of the same magnitude.
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
a. Develop hypotheses that can be used to test whether the population proportion of those
who will use the coupons is sufficient to go national.
b. The file Eagle contains the sample data. Develop a point estimate of the population
proportion.
c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the
promotion?
Answer:
a) Alternative hypothesis: the use of the coupons is isgnificantly higher than 10%.
Null hypothesis: the use of the coupons is not significantly higher than 10%.
The null and alternative hypothesis can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) Point estimate p=0.13
c) At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
Eagle should not go national with the promotion as there is no evidence it has been succesful.
Step-by-step explanation:
The question is incomplete.
The sample data shows that x=13 out of n=100 use the coupons.
This is a hypothesis test for a proportion.
The claim is that the proportion of coupons use is significantly higher than 10%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
The significance level is 0.05.
The sample has a size n=100.
The point estimate for the population proportion is the sample proportion and has a value of p=0.13.
[tex]p=X/n=13/100=0.13[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.0009}=0.03[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.13-0.1-0.5/100}{0.03}=\dfrac{0.025}{0.03}=0.833[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.833)=0.202[/tex]
As the P-value (0.202) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
PLS HELP (pic included)
hope it helps uh.......
Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
Answer:
$42.10
Step-by-step explanation:
Assuming that she did not yet buy a costume for herself, 800 dollars divided among 18 people plus herself is equal to $42.10 maximum per person.
Answer:
44.44
Step-by-step explanation:
800 didvided by 18.
Stuck Right now, Help would be appreciated :)
Answer:
C. c = (xv - x) / (v - 1).
Step-by-step explanation:
v = (x + c) / (x - c)
(x - c) * v = x + c
vx - vc = x + c
-vc - c = x - vx
vc + c = -x + vx
c(v + 1) = -x + vx
c = (-x + vx) / (v + 1)
c = (-x + xv) / (v + 1)
c = (xv - x) / (v + 1)
So, the answer should be C. c = (xv - x) / (v + 1).
Hope this helps!
Nika baked three loaves of zucchini bread. Each cake needed StartFraction 17 over 4 EndFraction cups of flour. Which expression shows the best estimate of the number of cups of flour that Nika used? 4 + 4 + 4 = 12 5 + 5 + 5 = 15 4 + 4 + 4 = 16 17 + 17 + 17 = 51
Answer:
(A)4 + 4 + 4 = 12
Step-by-step explanation:
Each of Nika's cake needed 17/4 cups of flour. Now, we know that:
[tex]\dfrac{17}{4}=4.25 \approx 4[/tex]
Therefore, for three loaves of bread, the best estimate of the number of cups of flour Nika used is:
4 + 4 + 4 = 12
The correct option is A.
Answer:
The correct answer is A.)4 + 4 + 4 = 12
Which of the following relations is a function?
A{(1, 3), (2, 3), (4,3), (9. 3)}
B{(1, 2), (1, 3), (1.4), (1,5)}
C{(5, 4), (-6, 5), (4, 5), (4, 0)}
D{(6,-1), (1, 4), (2, 3), (6, 1)}