Answer:
368 miles
Step-by-step explanation:
when we multiply 23 by 16 we get 368 miles .
23x16=368
Answer:
368 miles
Step-by-step explanation:
Formula:
Distance = gallons * miles per gallon
Givens
gallons: 16
miles per gallon: 23
Solution
distance = 16 * 23
distance = 368 miles
−30=5(x+1) solve for x pls help
Answer:
[tex] \boxed{\sf x = -7} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x: \\ \sf \implies - 30 = 5(x + 1) \\ \\ \sf - 30 =5(x+ 1) \: is \: equivalent \: to \: 5 (x + 1) = - 30: \\ \sf \implies 5(x + 1) = - 30 \\ \\ \sf Divide \: both \: sides \: of \: 5(x+ 1) = - 30 \: by \: 5: \\ \sf \implies \frac{5(x + 1)}{5} = - \frac{30}{5} \\ \\ \sf \frac{5}{5} = 1 : \\ \sf \implies x + 1 = - \frac{30}{5} \\ \\ \sf - \frac{30}{5} = - \frac{6 \times \cancel{5}}{ \cancel{5}} = - 6 : \\ \sf \implies x + 1 = - 6 \\ \\ \sf Subtract \: 1 \: from \: both \: sides: \\ \sf \implies x + (1 - 1) = - 6 - 1 \\ \\ \sf 1 - 1 = 0 : \\ \sf \implies x = - 6 - 1 \\ \\ \sf - 6 - 1 = - 7 : \\ \sf \implies x = - 7[/tex]
Answer:
[tex] \boxed{x = - 7}[/tex]
Step-by-step explanation:
[tex] \mathrm{ - 30 = 5(x + 1)}[/tex]
Distribute 5 through the parentheses
[tex] \mathrm{ - 30 = 5x + 5} [/tex]
Move constant to L.H.S and change its sign
[tex] \mathrm{ - 30 - 5 = 5x}[/tex]
Calculate
[tex] \mathrm{ - 35 = 5x}[/tex]
Swipe the sides of the equation
[tex] \mathrm{5x = - 35}[/tex]
Divide both sides of the equation by 5
[tex] \mathrm{ \frac{5x}{5} = \frac{ - 35}{5} }[/tex]
Calculate
[tex] \mathrm{x = - 7}[/tex]
Hope I helped!
Best regards!!
Find (f•g)(x) for the given functions: f(x) = 5/x and g(x) = 3 + x/5.
A rectangular piece of sheet metal has an area of 1200 in2. It is going to be bent into a cylinder with volume 600 in3. What are the dimensions of rectangular piece of sheet metal
Answer:
x=6.28 inches
y=191.08 inches
Step-by-step explanation:
Let the dimensions of the rectangle be x and y
Area of the rectangular sheet
x*y=1200 in^2}
x = circumference of the cylinder
This means x=2πr
Volume of a cylinder=πr^2h
h=y
Volume of the cylind=πr^2(y)=600 in^3
From x=2πr
r=x/2π
Substitute r=x/2π into Volume=πr^2(y)=600 in^3
We have,
Volume of the cylinder=πr^2(y)=600 in^3
π*(x/2π)^2(y)=600
(x^2/4π)y=600
Recall, x*y=1200
y=1200/x
Substitute y=1200/x into (x^2/4π)y=600
(x^2/4π)y=600
(x^2/4π)(1200/x)=600
1200x/4π=600
Multiply both sides by 4π
(x^2/4π)(1200/x)(4π)=600*4π
1200x=2400π
Divide both sides by 1200
1200x/1200 = 2400π/1200
x=2π
Substitute x=2π into y=1200/x
We have,
y=1200/2π
y=600/π
The dimensions are x=2π and y=600/π
Let π=3.14
x=2π
=2(3.14)
=6.28 inches
y=600/π
=600/3.14
=191.08 inches
The graph represents function 1 and the equation represents function 2:
Function 2 y = 4x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?
Greetings from Brasil...
In a linear function, the rate of change is given by M (see below).
F(X) = Mx + NM = rate of change
N = linear coefficient
The Function 2 has M = 4, cause
F(X) = 4X + 1
(M = 4 and N = 1)
For Function 1 we have a rate of change equal to zero, becaus it is a constant function... let's see:
M = ΔY/ΔX
M = (3 - 3)/(4 - 0)
M = 0/4 = 0
So, the Function 2 has 4 times more rate of change than the first
Your answer is two!!
The function s(V) = Negative RootIndex 3 StartRoot uppercase V EndRoot describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
This question is incomplete
Complete Question
The function s(V) = ∛V describes the side length, in units, of a cube with a volume of V cubic units.
Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
a) s > 0
b) s ≥ 4
c) s ≥ 8
d) s ≥ 16
Answer:
b) s ≥ 4
Step-by-step explanation:
From the above question, we are given Volume of the cube = 64cm³
We are given the function
s(V) = ∛V
Hence,
The range for the side length s =
s(V) ≥ ∛V
s(V) ≥ ∛64 cm³
s(v) ≥ 4 cm
Therefore, the reasonable range for s, the side length, in centimeters, of Jason’s cube
Option b) s ≥ 4
Answer:
s≥ 4
Step-by-step explanation:
Perform the indicated operation. 15b/4 * 8/9a^2b^2
Answer:
The simplified expression is [tex]\frac{10}{3 a^2 b}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{15b}{4} * \frac{8}{9a^2 b^2}[/tex]
Multiply the items in the numerator together ( 15b * 8 = 120 b). Also multiply the items in the denominator together ( 4 * 9a²b² = 36a²b²). The expression thus becomes:
[tex]= \frac{120b}{36 a^2 b^2} \\\\[/tex]
Divide both the numerator and the denominator by 12b:
[tex]= \frac{120b /12b}{36 a^2 b^2/12b}[/tex]
The expression finally becomes:
[tex]= \frac{10}{3 a^2 b}[/tex]
Answer:
Step-by-step explanation:
here u go
Transformations of exponential functions
Answer:
Since the transformation is made by shifting the function right, it is a horizontal transformation.
When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from five people are combined and the mixture tests negative, we know that all five individual samples are negative. Find the probability of a positive result for five samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.06.
Answer: 0.271
Step-by-step explanation:
Probability of complement of an even is 1 decreased by the probability of the event
P(At least one) =1 - P(none)
The probability that of testing negative is 0.9 because the probability of testing positive is 0.1
P( at least one) = 1 - P(none) = 1 - (0.93^3) = 0.271
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.
Answer:
John is 9, Brian is 6.
Step-by-step explanation:
I)
Let [tex]J[/tex] represent John's age and [tex]B[/tex] represent Brian's age.
John is three years older than Brian. In other words:
[tex]J=B+3[/tex]
The product of their ages is 54. Or:
[tex]JB=54[/tex]
II)
Write this as a quadratic by substituting:
[tex]JB=54\\(B+3)B=54\\B^2+3B-54=0[/tex]
III)
Solve the quadratic:
[tex]B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6[/tex]
Since age cannot be negative, Brian must be 6 years old right now.
John is three year older, so John is 9.
core: 0 of 1 pt
9 of 9 (0 complete)
HW Score: 0%, 0 of 9 p
.7.29
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Question Help
The supply function and demand function for the sale of a certain type of DVD player are given by S(p) = 140e 0.005p and D(p) = 448e -0.003p, where S(p) is the number
of DVD players that the company is willing to sell at price p and D(p) is the quantity that the public is willing to buy at price p. Find p such that D(p) = S(p). This is called
the equilibrium price.
The equilibrium price is about $
(Do not round until the final answer. Then round to two decimal places as needed.)
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Enter your answer in the answer box and then click Check Answer.
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Answer:
145.39
Step-by-step explanation:
The ratio of supply to demand will be 1 at the equilibrium price:
S(p)/D(p) = 1 = 140e^(0.005p)/(448e^(-0.003p))
448/140 = e^(0.005p -(-0.003p)) = e^(0.008p)
ln(448/140) = 0.008p . . . . . . . . . taking the natural log
p = ln(448/140)/0.008 ≈ 145.39
The equilibrium price is about $145.39.
questions:
1. name two parallel lines___________________
2. Name the transversal lines________________
3. Name a pair of alternante exterior angles____________
4. Name an angle that is congruent to <2____________
5. Name an angle that is supplementary to <2________________________
Answer:
a and b c because it's crossing both lines a and b 1 and 5 4 is congruent to 21 is supplementary to 2 since they form a 180° angleWhat additional information do you need to prove △ABC ≅ △DEF by the SSS Postulate? A. BC = EF B. AB = DE C. AC = DF
Answer:
AC = DF
Step-by-step explanation:
The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.
Calculate the pay for the following day of a
weekly time card given a wage of $14/hr.
Morning:
In 08:00
Out 12:00
Afternoon:
In 12:45
Out 17:30
pay = $[?]
Answer: $122.50
Step-by-step explanation:
In Out
8:00 12:00 = 4 hours
12:45 17:30 = 4.75 hours
Total 8.75 hours
8.75 hours x $14/hr = $122.50
Note: to subtract 12:45 from 17:30, borrow 1 hour from 17 and add 60 minutes to 30:
17:30 → 16:90
- 12:45 - 12:45
4: 45
4 hours 45 minutes = [tex]4\frac{3}{4}[/tex] = 4.75 hours
what is the point slope equation of a line with a slope 4 of a that contains the point (6, -2)?
Answer:
y+2 = 4(x-6)
Step-by-step explanation:
The point slope equation of a line is
y-y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line
y - -2 = 4( x-6)
y+2 = 4(x-6)
In 2010 polls indicated that 75% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2010?
We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year The p-value is 0.013
Which of the following interpretation of this p-value is valid?
A. The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B. There is a 1.3% chance that the null hypothesis is true.
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Answer:
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.
2x + 3 + 7x = – 24, what is the value of x?
14x + 3 = - 24
theeeeen I get stuck, HELP!
Answer:
-3
Step-by-step explanation:
2x + 3 +7x = -24
Add the X together
9x +3 = -24
Bring over the +3. [when you bring over change the sign]
9x = -24 -3
9x = -27
-27 divide by 9 to find X
therefore answer is
x= -3.
Hope this helps
Answer:
x = -3
Step-by-step explanation:
question is
2x + 3 + 7x = -24
First you combine the like terms
2x and 7x you can add them so it will be 9x
so it will then it will be like this:
9x + 3 = -24
now you take the 3 and send it to the other side, and right now the 3 is positive so when it goes to the other side it will turn into -3
so
9x = -24 -3
again now you combine the like terms
-24 -3 = - 27
now you have
9x = -27
now just divide each side by 9
x = -27/9
x = -3
Sorry if this doesnt help
Solve tan theta +1=-2tan theta
Answer:
[tex]\boxed{135\°,315\°}[/tex]
Step-by-step explanation:
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
[tex]\theta = 135+180n[/tex]
[tex]n[/tex] is any integer value.
The value of [tex]n[/tex] cannot exceed 1 or be less than 0, because the value of [tex]\theta[/tex] must be between 0 and 360 degrees.
[tex]\theta = 135+180(0)[/tex]
[tex]\theta = 135[/tex]
[tex]\theta = 135+180(1)[/tex]
[tex]\theta = 315[/tex]
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
(C) Junk Bonds, 13%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answer:
A. $22,223
B. $20,000
C. $20,000
Explanation:
The annual return of the retired couple's investment is called the yield in percentage.
A. If they go for Treasury bills which has a yield of 9%, to attain a return of at least $2,000 their investment must exceed $20,000. 9% of 22,223 = $2,000.07
B. . If they go for Corporate bonds option which has a yield of 11%, to attain a return of at least $2,000; 11% of 20,000 = $2,200
C. . If they go for Junk bonds option which has a yield of 13%, to attain annual return of at least $2,000; 13% of $20,000= $2,600
A researcher wishes to estimate the number of households with two cars. A previous study indicates that the proportion of households with two cars is 25%. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%?
A) 4.
B) 1132.
C) 1842.
D) 1382.
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0. What is the average speed of the car in miles per minute? What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes? PLEASE HELP
Answer:
Below
Step-by-step explanation:
The average speed is given by the following formula:
● V = d/t
● d is the distance covered
● t is the time spent to cover the distance d
■■■■■■■■■■■■■■■■■■■■■■■
Ava takes 8 minutes to go from mile marker 0 to mile marker6.
● the distance Ava traveled is 6 miles
● the time Ava spent to reach mile marker 6 is 8 minutes
So the average speed of Ava is:
● V = 6/ 8 = 3/4 = 0.75 mile per min
●●●●●●●●●●●●●●●●●●●●●●●●
Let's The equation of the line that links the number of milemarkers (n) and the time (t).
Ava went from mile marker 0 to mile marker 6.
At t=0 Ava just started travelling from mile marker 0 to 1.
Afrer 8 minutes,she was at mile marker 6.
So 8 min => 6 mile markers (igonring mile marker 0 since the distance there was 0 mile)
6/8= 0.75
Then n/t = 0.75
● n = 0.75 * t
Let's check
● n= 0.75*4 = 3
That's true since after 4 minutes Ava was at mile marker 3.
Which of the following ordered pairs satisfied the inequality 5x-2y<8
A) (-1,1)
B) (-3,4)
C) (4,0)
D) (-2,3)
Answer: A, B, and D
Step-by-step explanation:
Input the coordinates into the inequality to see which makes a true statement:
5x - 2y < 8
A) x = -1, y = 1 5(-1) - 2(1) < 8
-5 - 2 < 8
-7 < 8 TRUE!
B) x = -3, y = 4 5(-3) - 2(4) < 8
-15 - 8 < 8
-23 < 8 TRUE!
C) x = 4, y = 0 5(4) - 2(0) < 8
20 - 0 < 8
20 < 8 False
D) x = -2, y = 3 5(-2) - 2(3) < 8
-10 - 6 < 8
-16 < 8 TRUE!
A sample of size 60 from one population of weights had a sample average of 10.4 lb. and a sample standard deviation of 2.7 lb. An independent sample of size 100 from another population of weights had a sample average of 9.7 lb. with a sample standard deviation of 1.9 lb. Find a 95% confidence interval for the difference between the population means.
Answer:
z= 0.278
Step-by-step explanation:
Given data
n1= 60 ; n2 = 100
mean 1= x1`= 10.4; mean 2= x2`= 9.7
standard deviation 1= s1= 2.7 pounds ; standard deviation 2= s2 = 1.9 lb
We formulate our null and alternate hypothesis as
H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)
We set level of significance α= 0.05
the test statistic to be used under H0 is
z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂
the critical region is z > ± 1.96
Computations
z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100
z= 10.4- 9.7/ √ 7.29/60 + 3.61/100
z= 0.7/√ 0.1215+ 0.0361
z=0.7 /√0.1576
z= 0.7 (0.396988)
z= 0.2778= 0.278
Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0 at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.
Two similar data sets are being compared. The standard deviation of Set A is 4.8. The standard deviation of Set B is 6.5.
Answer:
The spread of the data in Set B is greater than the spread of the data in Set A.
Step-by-step explanation:
Just took the test :3
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
Which correlation coefficient could represent the relationship in the scatterpot
Answer:
D. -0.98
Step-by-step explanation:
Well it is a negative correlation and it is really strong but it is impossible to go pasit -1.
Thus,
the answer is D. -0.98
Hope this helps :)
Answer:
D. -0.98
Step-by-step explanation:
The correlation is a negative if the Y value decreases as the x value increases. It is not -1.43 because it is not decraeseing that fast.
A scrub nurse recorded the temperature in the operating theatre every two hours over a 12 hour period from noon to midnight. The results are shown in the following line graph
NoAnswer:
Step-by-step explanation:
Cause I’m good
Faizan buys a car for £2000.Its value depreciates by 2% each year. How much is it worth after 1 year?
Answer:
£1960
Step-by-step explanation:
Step 1.
2% = 100% ÷ 50
Step 2.
£2000 ÷ 50 = £40
Step 3.
£2000 - £40 = £1960
Which of the following is equivalent to (3)/(x)=(6)/(x-4)
Answer:
[tex]3(x - 4) = 6x[/tex]Option A is the correct option.
Step-by-step explanation:
[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]
Apply cross product property:
[tex]3(x - 4) = 6 \times x[/tex]
[tex]3(x - 4) = 6x[/tex]
Hope this helps...
Best regards!!
Answer:
3 * (x - 4) = 6 * x.
Step-by-step explanation:
3 / x = 6 / (x - 4)
3 * (x - 4) = 6 * x
3x - 12 = 6x
6x = 3x - 12
6x - 3x = -12
3x = -12
x = -4.
Hope this helps!
Find the surface area of the triangular prism (above) using its net (below).
Answer:
96 square units
Step-by-step explanation:
The surface area of the prism can be calculated using its net.
The net consists of 3 rectangles and 2 triangles.
The surface area = area of the 3 rectangles + area of the 2 triangles
Area of 3 rectangles:
Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units
Area of the middle triangle = L*B = 7*6 = 42 square units.
Area of the 3 triangles = 42 + 42 = 84 square units.
Area of the 2 triangles:
Area = 2(½*b*h) = 2(½*6*2) = 6*2
Area of the 2 triangles = 12 square units
Surface area of the triangular prism = 84 + 12 = 96 square units.
Answer:
It's 96 unit2
Step-by-step explanation:
I just do it in khan and it's correct
01:
Which expression can be used to model the phrase the sum of three and a number?
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation