we have the next equivalence
1 gallon - 128 oz
5 gallon - x
(5 gallon times 128 onz )/ 1 gallon = 640 onz
6 ÷ 3/4 ? with an explanation..
The given expression is
6 ÷ 3/4
If we flip 3/4 so that it becomes 4/3, the division symbol will chane to multiplication. It becomes
6 * 4/3
= 24/3
= 8
Triangle ABC is inscribed in the circle below. Using the measurements provided in the diagram, find the measure of arc AB.
Given: A triangle ABC inscribed in a circle as shown in the shown image in the question
To Determine: The measure of the arc AB
Solution
Re-draw the diagram
Let the center of the circle be O as shown in the image above
It can be seen that the angle subtended by the arc BC is the same as angle BOC
Using the circle theorem, the angle at the center is twice angle at the circumference.
The angle subtended at the circumference by the arc BC is angle BAC
Therefore
[tex]\angle BOC=2\times\angle BAC[/tex][tex]\begin{gathered} \angle BOC=112^2 \\ Therefore \\ 2\times\angle BAC=112^0 \\ \angle BAC=\frac{112^0}{2} \\ \angle BAC=56^0 \end{gathered}[/tex]Note: The angle A, angle B and angle C formed the interior angles of the triangle ABC. Therefore
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ 56^0+65^0+\angle C^0=180^0 \\ 121^0+\angle C=180^0 \\ \angle C=180^0-121^0 \\ \angle C=59^0 \end{gathered}[/tex]It can be observed that angle C is the angle subtended by arc AB at the circumference and angle AOB is the angle subtended by the arc AB at the center. Using the circle theorem that angle subtended at the center is twice angle subtended at the circumference
Therefore
[tex]\begin{gathered} \angle AOB=2\times\angle C \\ \angle AOB=2\times59^0 \\ \angle AOB=118^0 \end{gathered}[/tex]Hence, the measure of arc AB is 118⁰
what is the midpoint of line segment AB when A(-2,10) and B(6,-4)
(2, 3)
Explanations:The coordinates of the midpoint (a, b) of the line with the endpoints (x₁, y₁ ) and (x₂, y₂) is given by the formulae:
[tex]\begin{gathered} a\text{ = }\frac{x_1+x_2}{2} \\ b\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]The line segment AB has endpoints A(-2,10) and B(6,-4)
Therefore:
x₁ = -2, y₁ = 10, x₂ = 6, y₂ = -4
Substitute these values into the formulae for the coordinates of the midpoints
[tex]\begin{gathered} a\text{ = }\frac{-2+6}{2} \\ a\text{ = }\frac{4}{2} \\ a\text{ = 2} \\ b\text{ = }\frac{10+(-4)}{2} \\ b\text{ = }\frac{10-4}{2} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]The midpoint of the line segment AB is therefore (2, 3)
Factor. 8y +16 what is the answer
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
8y + 16
Step 02:
factor:
8y + 16 = 8 (y + 2)
The answer is:
8 (y + 2)
1. A random sample of 25 of the 400 members of the Bigtime TheaterCompany is surveyed about how many plays each has acted in. Make a boxplot of the data. Then use the box plot to make a qualitative inferenceabout the population. 3, 5, 5, 3, 4, 4, 1, 3, 6, 10, 1, 3, 4, 5, 1, 2, 4, 2, 3, 2, 5,5, 5, 5, 6
1) Let's begin by finding the Quartiles as well as the outliers, with the given data :
[tex]\begin{gathered} 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4 \\ Median\:of\mathrm{\:}1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4=Q_1=\quad2.5 \\ \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ Median(Q_2)=4 \\ \\ Q_3 \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ 5 \end{gathered}[/tex]Now, that we know the quartiles, let's find the IQR, the interquartile range subtracting from the Upper Quartile the Lower one
a model of a house is shown. What is the perimeter of the model?
STEP-BY-STEP EXPLANATION:
As you can see from the question given, the fgure is a combination of an Isosceles triangle and a rectangle.
Supposed that the future price p(t) of a certain item is given by the following exponential function.inthis function, p(t) is measured in dollars and t is the number of year's from today. p(t)= 2500 (1.026)t
Answer:
Initial price of the item = 2500
The function represents growth
The percent by which the price changes each year is 2.6%
Explanation:
The given function is expressed as
P(t) = 2500(1.026)^t
Recall, the exponential growth function is expressed as
P(t) = Po(1 + r)^t
where
Po is the initial value
P(t) is the future value
r is the growth rate
By comparing both functions,
Po = 2500. Thus,
Initial price of the item = 2500
Also,
1 + r = 1.026
Since 1.026 is greater than 1,
The function represents growth
r = 1.026 - 1
r = 0.026
This means that the growth rate is 0.026. We would convert it to percentage by multiplying by 100. It becomes
0.026 x 100 = 2.6%
The percent by which the price changes each year is 2.6%
3+5=5+ 3•5=5•2+(-2)=0TRUE OR FALSE ? ( for all three of them )
Take into account that commutative property is present for addition and multiplication operations, then, you have:
3+5=5+3 TRUE
3·5 = 5·3 TRUE
The inverse addition of a number consists in adding the same numbers but with opposite signs, then, you have:
2 + (-2) = 0 TRUE
Given f (x)=9.2x +11, what is f (12)? If it does not exist, enter DNE
Given:-
[tex]f(x)=9.2(x)+11[/tex]To find:-
[tex]f(12)[/tex]So to find the required value. we substitute 12 for x. so we get,
[tex]\begin{gathered} f(x)=9.2(x)+11 \\ f(12)=9.2(12)+11 \\ f(12)=110.4+11 \\ f(12)=121.4 \end{gathered}[/tex]So the required solution is 121.4
In circle H with mZGHJ = 68°, find the angle measure of minor arc GJ .HG
We have to find the measure of the minor arc GJ.
For angles that have a vertex at the center of the circle, they have the same measure than the arc:
Then, as m
Answer: mGJ = 68°
nA cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicularto the baseThe cross section can be which of these shapes? Select three options.squaretriangletrapezoidcirclenon-square rectangleSave and ExitNextSubnetMaths and retum
The base of the pyramid is a square. If the crosssection is parallel to the base, the shape formed would be that of the base and it is a square
If the crosssection is perpendicular to the base, the shape formed would be that of the triangular face and it is a traingle
The other shape that can be formed when the cross section is perpendicular to the base but not actually at the vertex, the shape formed is a trapezoid
The shapes are
square
triangle
trapezoid
A telemarketer's computer selects phone numbers at random. The telemarketer has recorded the number of respondents in each age bracket for one evening in the following table. What is the probability that the next respondent is between 18 and 35? Enter a fraction or round your answer 4 decimal places,if necessary.Under 18= 2618-25=3026-35=4036-45=60Over 45= 51
The probability of an event e occurring can be found using the formula:
[tex]P(an\text{ event e occurring \rparen = }\frac{Number\text{ of occurrence of the event}}{Total\text{ number of occurrence}}[/tex]Required: The probability that the next respondent is between 18 and 35
Number of respondents between the ages of 18 and 35 = 30
Total number of respondents:
[tex]\begin{gathered} =\text{ 26 + 30 + 40 + 60 + 51} \\ =\text{ 207} \end{gathered}[/tex]Hence, the probability that the next respondent is between 18 and 35 is:
[tex]\begin{gathered} P=\text{ }\frac{30}{207} \\ =\text{ 0.144927} \\ \approx\text{ 0.1449} \end{gathered}[/tex]Answer: 0.1449
The temperature at 2 A.M. was -5.5°C. The temperature changed an average of -2.1°C each hour for 4 hours and then changed an average of 3.2°C each hour for 3 hours. What was the temperature at 9 A.M.?
To obtain the temperature at 9A.M., the following steps are necessary:
Step 1: Find the total temperature change at the end of the 4 and 3 hour periods, as follows:
At the end of 4 hours, the total temperature change is:
[tex]\text{total temperature change = average temperature }\times\text{ nu}mber\text{ of hours}[/tex]Thus:
[tex]\begin{gathered} \text{total temperature change = -2.1}\times\text{4} \\ \Rightarrow\text{total temperature change = }-8.4^oC \end{gathered}[/tex]Thus, after 4 hours, the temperature that was initially at -5.5 degrees celsius at 2 A.M. becomes:
[tex]f\text{inal temperature - initial temperature = total temperature change}[/tex]Thus, after 4hours, that is when it is 6 A.M, the temperature is:
[tex]\begin{gathered} f\text{inal temperature - initial temperature = total temperature change} \\ \Rightarrow finaltemperature-(-5.5^oC\text{) = }-8.4^oC \\ \Rightarrow finaltemperature\text{ = }-8.4^oC+(-5.5^oC\text{)} \\ \Rightarrow finaltemperature\text{ = }-8.4^oC-5.5^oC \\ \Rightarrow finaltemperature\text{ = }-13.9^oC \end{gathered}[/tex]Thus, at 6 A.M (after 4 hours) the temperature is -13.9 degrees celsius.
--Finally, we find the temperature at 9 A.M. (after another 3 hours), as follows:
At the end of another 3 hours, the total temperature change is:
[tex]\text{total temperature change = average temperature }\times\text{ nu}mber\text{ of hours}[/tex]Thus:
[tex]\begin{gathered} \text{total temperature change = 3.2}\times\text{ 3} \\ \Rightarrow\text{total temperature change =9}.6^oC \end{gathered}[/tex]After another 3 hours, the temperature that was initially at -13.9 degrees celsius at 6 A.M. becomes the following at 9 A.M:
[tex]\begin{gathered} f\text{inal temperature - initial temperature = total temperature change} \\ \Rightarrow f\text{inal temperature - }(-13.9^oC\text{) = 9.6}^oC \\ \Rightarrow f\text{inal temperature = 9.6}^oC+(-13.9^oC\text{)} \\ \Rightarrow f\text{inal temperature = 9.6}^oC-13.9^oC \\ \Rightarrow f\text{inal temperature = -4.3}^oC \end{gathered}[/tex]IN CONCLUSION, therefore, the temperature at 9 A.M is - 4.3 degree celsius
Find the product.
9 x 105
Answer:
945
Step-by-step explanation:
I have to type more to send this but thats the answer because
Which is more, 7 miles or 36,956 feet?
Conversion factor
1 mile = 5280 ft
If we have 7 miles,
7 miles x 5280 ft per mile = 36,960 ft
Answer:
Thus 7 miles is greater than 36,956 feet
Consider the line y=9x-3.Find the equation of the line that is perpendicular to this line and passes through the point (-8, – 5).Find the equation of the line that is parallel to this line and passes through the point (-8, -5).
step 1
Find the slope of the given line
y=9x-3
the slope is m=9
step 2
Remember that
If two lines are perpendicular, then their slopes are negative reciprocal
that means
the slope of the perpendicular line is
m=-1/9
step 3
Find the equation of the line that is perpendicular to this line and passes through the point (-8, – 5).
we have
m=-1/9
point (-8,-5)
the equation in slope-intercept form
y=mx+b
substitute and solve for b
-5=(1/9)(-8)+b
-5=-(8/9)+b
b=-5+8/9
b=-37/9
y=-(1/9)x-37/9step 4
Find the equation of the line that is parallel to this line and passes through the point (-8, -5).
Remember that
If two lines are parallel, then their slopes are equal
the slope of the parallel line is
m=9
the equation in slope-intercept form
y=mx+b
substitute and solve for b
-5=9(-8)+b
-5=-72+b
b=67
therefore
y=9x+67your job in a moving company is to fill quart sized bottles of oil from a full 30 gallon oil drum. then you are to pack 8 quart bottle in a case to ship to a store. how many full cases of oil can you get from a full 30 gallon drum of oil?3cases7 cases15 cases16 cases
15 cases
1) Consider that 1 gallon corresponds to 4 quarts. So we can write out:
30 gallon = 120 quarts
8-quart bottle per case
2) So we have in each case 8-quart bottles. Since we have 120 quarts then, let's divide it by the capacity of the case:
[tex]\frac{120}{8}=15[/tex]3) Hence, we'll have 15 full cases with those 30 gallons (120 quarts) bottles of oil.
Solve for X:-6x + 2 = 5x + 5
Answer:
x = -3/11
Explanation:
The initial equation is:
-6x + 2 = 5x + 5
To solve the equation, we need to subtract 5 from both sides of the equation, so:
-6x + 2 - 5 = 5x + 5 - 5
-6x - 3 = 5x
Then, add 6x to both sides of the equation:
-6x - 3 + 6x = 5x + 6x
-3 = 11x
Finally, divide both sides by 11, so:
-3/11 = 11x/11
-3/11 = x
Therefore, the answer is x = -3/11
hi you buy a pair of scissors that cost $4.55 and two packs of gum that cost $0.75 each. how much money would you need to buy there items?
Answer:
You would need $10.60 to buy these items
Step-by-step explanation:
You buy two scissors, each for $4.55. Two packs of gum, each for $0.75.
Total: 2*4.55 + 2*0.75 = 9.10 + 1.50 = $10.60
You would need $10.60 to buy these items
You pick a card at random. Without putting the first card back, you pick a second card at random.1234What is the probability of picking a 4 and then picking a number less than 3?Simplify your answer and write it as a fraction or whole number.
The probability of picking a 4 in the first selection is:
[tex]P(4)=\frac{1}{4}[/tex]Now we only have the cards 1, 2, and 3 in the deck.
The probability of picking a number less than 3, that is, 1 or 2 is:
[tex]P(\lt3)=\frac{2}{3}[/tex]The combined (dependent) probability is the product of the individual probabilities:
[tex]P=\frac{1}{4}\cdot\frac{2}{3}=\frac{1}{6}[/tex]The probability is 1/6
a box has a length of 6X inches the width equal 1/3 the lamps in the height equals half the length of the volume equals 972 cubic inches what does x equal?
The length of the box is 6x inches
The width of the box is 1/3 of the length, that is:
1/3 * 6x = 2x inches
The height of the box is 1/2 of the length, that is:
1/2 * 6x = 3x inches
The volume of the box is 972 cubic inches.
The volume of a box (rectangular box) is given as:
V = L * W * H
where L = length, W = width, H = height
This means that:
V = 6x * 2x * 3x
[tex]\begin{gathered} 972=36x^3 \\ \Rightarrow x^3\text{ = }\frac{972}{36} \\ x^3\text{ = 27} \\ \Rightarrow\text{ x = }\sqrt[3]{27} \\ x\text{ = 3} \end{gathered}[/tex]Which random variable for each distribution below would be discrete?A the maximum height reached by a modelrocket on each launchB the weight of packages shipped each weekby the postal serviceCDthe number of emails sent to your computerthe amount of snow that falls in a town peryearper week
The answer is D cause you can not send half of an email
Write an equation of the line through (2,5) and parallel to y=3x-8. Write the Equation in the form x=a, y=b, or Y=MZ+b
The equation of the given line is
y = mx + c
where
m = slope
c = y intercept
The equation of the given line is
y = 3x - 8
By comparing both equations,
m = 3
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of 3 is - 1/3. Thus, the slope of the perpendicular line passing through (2, 5) is - 1/3
We would fnd the y intercept, c by substituting m = - 1/3, x = 2 and y = 5 into the slope intercept equation. We have
5 = - 1/3 * 2 + c = - 2/3 + c
c = 5 + 2/3 = 17/3
Thus, the equation of the perpendicular line is
y = - x/3 + 17/3
Find the linear function such that f(-1)=7 and f(4)=-5
Hello, I need some help with this precalculus question for my homework, please HW Q6
Explanation
let's remember some properites of the logarithms:
[tex]\begin{gathered} \log_bM-\log_bN=\log_b(\frac{M}{N}) \\ \log_aM=b\text{ , M= a}^b \end{gathered}[/tex]so
Step 1
[tex]\log_(2x+7)=1+\log_(x-8)[/tex]a)
[tex]\begin{gathered} \log_(2x+7)=1+\log_(x-8) \\ subtract\text{ }\log_(x+8)\text{ in both sides} \\ log(2x+7)-log(x-8)=1+log(X-8)-log(x-8) \\ \begin{equation*} log(2x+7)-log(x-8)=1 \end{equation*} \\ apply\text{ the propery} \\ log(\frac{2x+7}{x-8})=1 \end{gathered}[/tex]b)now, convert the logarith into its exponential form( second property )
[tex]\begin{gathered} log(\frac{2x+7}{x-8})=1 \\ so\text{ } \\ \frac{2x+7}{x-8}=10^1 \\ \frac{2x+7}{x-8}=10 \end{gathered}[/tex]c) finally, isolate x
[tex]\begin{gathered} \frac{2x+7}{x-8}=10 \\ Multiply\text{ both sides by \lparen x-8\rparen} \\ \frac{2x+7}{x-8}*(x-8)=10(x-8) \\ 2x+7=10x-80 \\ subtract\text{ 2x in both sides} \\ 2x+7-2x=10x-80-2x \\ 7=8x-80 \\ add\text{ 80 in both sides} \\ 7+80=8x-80+80 \\ 87=8x \\ divide\text{ both sides by 8} \\ \frac{87}{8}=\frac{8x}{8} \\ x=\frac{87}{8},\text{ x}\in\langle8,\infty\rangle \end{gathered}[/tex]so, the answer is
[tex]A)\frac{87}{8}[/tex]I hope this helps you
Erwin spends at least $11.50 on lunch every day. Write an inequality to represent how much Erwin spends. A. L < $11.50 B. L >$11.50 C. L≤ $11.50 D. L ≥ $11.50
Answer:
D. L ≥ $11.50
Explanation:
If Erwin spends at least $11.50 on lunch, this means that:
• Erwin can spend ,exactly(=), $11.50; or
,• Erwin can spend ,more than(>), $11.50
Combining the two signs gives: ≥
An inequality to represent how much Erwin spends will then be:
[tex]L\ge\$11.50[/tex]The correct choice is D.
Express your answer as a polynomial in standard form.f(x) = x + 10g(x) = 2?= 2? + 2x – 7Find: (fog)(x)
Given function f and g, we can write:
[tex](f\circ g)(x)=f(g(x))[/tex]This means that we can just substitute g(x) into f to obtain the result. So let's do that:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)+10=(x^2+2x-7)+10 \\ (f\circ g)(x)=x^2+2x-7+10 \\ (f\circ g)(x)=x^2+2x+3 \end{gathered}[/tex]This already is in the standard form, so that is the answer.
Which of the following statement about each monomial is true? (Assume x is the variable) I. (3x/4)^2 is a second-degree monomial with coefficient 3/4. II. -32 is a zeroth-degree monomial with coefficient -32. III. (2/x)is a third-degree monomial with coefficient 8. (A) I and II (B) I and III(C) II only (D) II and III
I. (3x/4)^2 is a second-degree monomial with coefficient 3/4
[tex](\frac{3x}{4})^2=\frac{9}{16}x^2[/tex]So, it is a second degree monomial with coefficient 9/16 and not 3/4 as stated in the statement.
The statement is wrong.
II. -32 is a zeroth-degree monomial with coefficient -32.
-32 is surely a zero degree monomial with coefficient -32.
The statement is Correct
III. (2/x)is a third-degree monomial with coefficient 8.
2/x is not a third degree monomial.
the statement is wrong
The correct answer is (C) II only
5.What is the measurement of <1 that makes line a parallel to line b?5x+630+ 2x)
Weare asked to find which measurement of angle "1" will make the lines a and b parallel in the following image:
So, if we want the lines a and b to be parallel, then the alternate internal angles labeled 5 x + 6 and 30 + 2 x must be EQUAL. That is:
5 x + 6 = 30 + 2 x
solving for "x", we proceed to subtract 2 x from both sides:
5 x - 2 x + 6 = 30
3 x + 6 = 30
subtract 6 from both sides:
3 x = 30 - 6
3 x = 24
divide both sides by 3:
x = 24 / 3 =
x = 8
Then, if x = 8 degrees, then the supplementary angle to angle <1 is:
30 + 2 x = 30 + 2 (8) = 30 + 16 = 46 degrees
Then angle <1 is 180 degrees minus 46 degrees, that is:
<1 = 180 - 46 = 134 degrees.
<1 measures 134 degrees.
i need help i have no idea how to do this
SOLUTION
Prove 1
[tex]\begin{gathered} AB=3y-1 \\ BC=7y \\ AC=29 \\ AB+BC=AC \\ 3y-1+7y=29 \\ 3y+7y=29+1\text{ (after collecting like terms)} \\ 10y=30 \\ y=\frac{30}{10} \\ \\ y=3 \\ AB=3y-1 \\ \text{then} \\ AB=3(3)-1 \\ AB=9-1 \\ \text{Therefore } \\ AB=8 \end{gathered}[/tex]Prove 2
[tex]\begin{gathered} AB=AC-BC_{} \\ AB=29-7y \\ We\text{ have found y as 3} \\ AB=29-7(3) \\ AB=29-21 \\ AB=8 \end{gathered}[/tex]