Answer:
Step-by-step explanation:
From the question, I couldn't really tell what the chart looks like, so I am guessing it looks like this:
Sidewalk 1:
x | y
2 | 17
0 | 5
Sidewalk 2:
x | y
1 | 20
3 | 26
Part a.
Now, we have to write the equation for sidewalk 1 in slope-intercept form.
Slope-intercept form is represented as this: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. Because this is true for all values on the line, we can plug in values of the chart for Sidewalk 1.
[tex]17=2m+b\\5=0m+b[/tex]
Subtracting the second equation from the first, we have
[tex]12=2m[/tex], and [tex]m = 6[/tex].
Now, we can just plug 6 back into the first equation to get:
[tex]17=2(6)+b[/tex] to get [tex]17 = 12 + b[/tex], and then [tex]b = 5[/tex].
Now, we can just rewrite slope intercept form for Sidewalk 1 to have
[tex]y=6x+5[/tex].
Part b.
Point-slope form is represented as [tex]y-y_1=m(x-x_1)[/tex], where x and y are the coordinates of one point, and x1 and y1 are the coordinates of another point on the line. Because the chart represented for Sidewalk 2 includes a point, namely [tex](1, 20)[/tex] and [tex](3, 26)[/tex], we can plug this in and solve for the slope:
[tex]26-20=m(3-1)[/tex]
This is it in point-slope form. Because the second part of the question asks us to convert to slope-intercept form, we must solve for the slope, or m.
Expanding, we have [tex]26-20=3m-m[/tex]
Combining like terms, we have [tex]6 = 2m[/tex], and then [tex]3 = m[/tex]. Now, we need to plug a point and the slope back into point-slope form, not needing another point. We choose [tex](1, 20)[/tex], even though [tex](3, 26)[/tex] works just as well.
[tex]y-20=3(x-1)[/tex]
Expanding, we have [tex]y-20=3x-3[/tex]
Adding 20 to both sides, we have [tex]y=3x+17[/tex]
Part c. and d.
We see that both equations do not have the same slope, so then they are not parallel, meaning they don't have no solutions. If they have a solution, we can set them equal to each other.
[tex]3x+17=6x+5[/tex]
Subtracting 3x, we have [tex]17=3x+5[/tex]
Subtracting 5, we have [tex]12 = 3x[/tex]
Dividing by 3, we have [tex]x = 4[/tex].
Because there is no x = x, or anything like that, the solution does not have infinite solutions and therefore has one solution, meaning it is consistent independent.
How much would $125 invested at 8% interest compounded continuously be
worth after 16 years? Round your answer to the nearest cent.
A(t)= Poet
A. $428.24
B. $285.00
C. $449.58
D. $367.26
c$449.58
hfufhfthcuxjyfus4hxtstcyztf
Central/Inscribed angles pls help with work <3
Answer:
Step-by-step explanation:
Arc angle KLM will be twice ∠KSM = 210°
Arc angle ML will be 210 - 130 = 80°
Arc angle LMS will be twice ∠LKS = 160°
Arc angle SM will be Arc angle LMS - ML = 160 - 80 = 80°
I am having a hard time on solving this question x4−85=−92 does someone know how to explain it?
Answer:
X equals positive -1.75
Step-by-step explanation:
because X is muliplying by the common number attached to it (4)
-1.75 times 4 equals -7
thus being -7-85= -92
Answer:
well you have to solve for X so -1.75 times 4 equals -7 then solve. so your answer would be- X equals positive -1.75
A group of preschoolers has 63 boys and 27 girls. What is the ratio of boys to all children (lowest form)?
Answer:
7 boys to 10 all children
What is the measure of QTR?
What is the measure of PTR?
Answer:
QTR is 36
PTR is 62
Step-by-step explanation:
P+R+T=180
The circumference of a circular garden is 72.22 feet. What is the radius of the garden?
Answer:
36.11 feet
Step-by-step explanation:
If the circumfrence goes across the circle, and the radius goed halfway, substitute the measuremants. C/2. So, divide 72.22 by 2 and you get 36.11 feet!
Evaluate the expression for the given variable 4y-12, when y =7
Answer:
16
Step-by-step explanation:
y = 7
4(7)-12
28-12 = 16
I Need help with 4-7
Answer:
Step-by-step explanation:
4) parallel because 118° is a supplement to 62° and the corresponding angles are both 118°
5) NOT parallel. The labeled angles sum to 120° and would sum to 180° for parallel lines.
6) NOT parallel. see pic.
If parallel, extending a line to intersect ℓ₁ makes an opposite internal angle which would also be 48°. The created triangle would have its third angle at 180 - 90 - 48 = 42° which is opposite a labeled 48° angle, which is false, so the lines cannot be parallel
7)
b = 78° as it corresponds with a labeled angle above it
a = 180 - 78 = 102° as angles along a line from a common vertex sum to 180
f = is an opposite angle to 180 - 78 - 44 = 58° as angles along a line from a common vertex sum to 180
e = 180 - 90 - 64 = 26° as angles along a line from a common vertex sum to 180
c = 58° as it corresponds with f
d = 180 - 58 = 122° as angles along a line from a common vertex sum to 180
elect all the correct answers.
A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time.
After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments.
Which statements about this study are true?
This study uses blinding.
This study uses blocking.
This study uses a control group.
This study uses a repeated measures design.
This study uses random sampling.
this study uses random sampling
this study uses a control group
this study uses a repeated measures design
plato/edmentum
Answer:
This study uses a control group. This study uses a repeated measures design.
The width of a triangle is six more than twice the height. The area of the triangle is 88in2. Find the height and width of the triangle.
Answer:
w = 22 in, h = 8 in.
Step-by-step explanation:
Reading the problem, I immediately see two equations. This hints me towards a system of equations problem.
Statement 1 is The width of a triangle is six more than twice the height.
The width (w) of a triangle is (=) six (6) more (+) than twice (2) the height (h).
Equation 1: w = 6 + 2h
Statement 2 is The area of the triangle is 88 in2.
The formula for the area of a triangle is [tex]\frac{wh}{2}[/tex]. So, we get our second equation.
Equation 2: wh/2 = 88
We see that we have the same number of equations as unknowns, two. This is important as it lets us know that we can find two unknowns in the two equations. If there are more unknowns than equations, then we cannot find the values of all the variables. Look for another equation in the problem. However, if the # equations greater than or equal to number of unknowns, then we are ready to start solving! So, we can now move to solving.
Equation 1 isolates one of the unknowns (w). So, we can replace w in the second equation with the right side of eq 1. Then, we simplify for h.
[tex]\frac{wh}{2} = 88[/tex]
[tex]\frac{(6 + 2h)h}{2} = 88[/tex]
[tex]\frac{6h + 2h^2}{2} = 88[/tex]
[tex]6h + 2h^2 = 176[/tex]
[tex]2h^2 + 6h - 176 = 0[/tex]
[tex]h = -11, 8[/tex] (assuming you know how to solve quadratics)
Since we know that heights of triangles cannot be negative, we find that [tex]h = 8[/tex] in.
For the final step, we plug [tex]h[/tex] into our first equation to find [tex]w[/tex].
[tex]w = 6 + 2h[/tex]
[tex]w = 6 + 2(8)[/tex]
[tex]w = 6 + 16[/tex]
[tex]w = 22[/tex]
So, the answer is w = 22 in, h = 8 in.
To check if we were right, we can plug the values into both equations to see if they are equal. I will skip equation 1 since we used that equation "as-is" to find w.
[tex]\frac{wh}{2} = 88[/tex]
[tex]\frac{22 * 8}{2} = 88[/tex]
[tex]11 * 8 = 88[/tex]
[tex]88 = 88[/tex]
The solution checks out!
The initial population of a town is 3500, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Answer:
8 years = 5600
Step-by-step explanation:
10 years = 3500x2= 7000
1 year = 7000/10 = 700
1 year = 700
8 years = 700x8 = 5600
What is negative 10 divided by .22
Answer:
That would be negative 45 or - 45
Please correct me if im wrong
it is the onion of set of whole numbers and the opposition of the set counting or natural numbers A. integers B. inverse C. Positive D. Negative
integers is your answer
It takes Shawn 4 more hours to stain a deck than Michelle. Together it takes them 4.8 hours to complete the work. How long would it take Shawn to stain the deck by himself?
Answer:
4.4 hours
Step-by-step explanation:
It would take Shawn 4.4 hours, as this would give a time of .4 hours to Michelle, totaling 4.8 hours
7.
Find all solutions to the following triangle. (Round your answers for angles A, C, A', and to the nearest minute. Round your answers for sides a and a'to two decimal places. If either triangle is not
possible, enter NONE In each corresponding answer blank.)
B = 65° 20', b = 5.38 inches, c = 4.88 inches
First triangle (assume C greater than or equal to 90°):
A= ____ degrees ____’
C=____ degrees ____’
a= ____ in
The measures of the angles and the lengths of the sides of the triangle can
be found using sine rule.
The correct responses are;
A = 59 degrees 9'C = Nonea = 5.083 in.Reasons:
The given parameter are;
∠B = 65°20', b = 5.38 inches, c = 4.88 inches
∠C ≥ 90°
By sine rule, we have;
[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{4.88}{sin(\angle C)}}[/tex]
[tex]sin(\angle C) = \mathbf{ \dfrac{sin(65^{\circ} 20') \times 4.88}{5.38}}[/tex]
[tex]\angle C = arcsin \left(\dfrac{sin(65^{\circ} 20') \times 4.88}{5.38} \right) \approx \mathbf{ 55.517 ^{\circ}}[/tex]
∠C = 55.517° < 90°, therefore, the correct response is; None
[tex]\dfrac{sin(65^{\circ} 20')}{5.38} = \dfrac{4.88}{sin(\angle C)}[/tex]
∠A = 180° - 65°20' - 55.517° = 59.15° = 59°9'
∠A = 59°9'
Therefore;
[tex]\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{a}{sin(59.15^{})}}[/tex]
[tex]a = \dfrac{5.38 \times sin(59.15^{\circ}) }{sin(65^{\circ} 20')} \approx \mathbf{ 5.083}[/tex]
a ≈ 5.083 inches
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5(9/12−1/4)+0.5 pls answer correctly
Answer:
3
Step-by-step explanation:
5(9/12 -1/4) +0.5
= 5(9/12 -3/12) +1/2 . . . . . . express the fractions using a common denominator
= 5(6/12) +1/2 . . . . . . . add the fractions
= 5(1/2) +1/2 . . . . . . reduce the result
= (5 +1)(1/2) . . . . factor out 1/2 (easier than adding mixed numbers)
= 6/2 = 3
_____
A calculator can be a useful tool for evaluating numerical expressions.
x+3-3= -6
its my quick hot sauce
The Bruce family set out 8 0’clock in the morning. They arrived at the old port of Ambertini at 09:05. How long their journey took?
pls
Answer:
1hr 5 minutes
Step-by-step explanation:
9hrs 5mins-8 hrs=1 hr 5 mins
mark me brainliest plz if you are helped
Complete the equation for the line shown in the graph. (-1,-2) (0,1) (1,4)
Explain two ways you can benchmark percents to find 60% of 280
Answer:
The most common benchmark percents are 0%, 10%, 25%, 50%, 75% and 100%.
To find 60% of 280 we first find 10% of 280 which is 28. 6 x 28 = 168.
To find 60% of 280 we first find 50% of 280 which is 140. Now we add 10% which we calculated before: 140 + 28 = 168.
Answer:
Step-by-step explanation:
Explain two ways you can benchmark percents to find 60% of 280
1) 280 : 100 * 60 = 168
2) 280 * 0.6 = 168
–4x – 5 + 2x = –11
i need help solving for x in this equation
Answer:
x is 3
Step-by-step explanation:
-2x is -6
2x is 6
x is 3
Answer:
X=3
Step-by-step explanation:
-4(3)=-12
-12-5=-17
2(3)=6
-17+6=-11
[tex]{ \pink{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} } \sf \pink\int_{ 0 }^{x_{2}... \int_{ 0 }^{x_{99}}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/tex]
︎︎︎︎︎︎︎
Step-by-step explanation:
[tex]\small{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} \int_{ 0 }^{x_{2}}... \int_{ 0 }^{x_{99}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/tex]
[tex]\small{{ \displaystyle\tt = - \int_{0}^{1} \int_{0} ^{ x_{1}} \int_{ 0 }^{x_{2}}... \int_{ 0 }^{x_{98}} \sum_{n = 1}^{ \infty \frac{}{} \frac{}{} } \frac{1}{n} \int_{0}^{x_{99}} {x}^{n}_{100} \: dx_{100}...dx_{1} }}[/tex]
[tex]{{ 0 }^{x_{98}} \frac{{x}^{n + 1}_{99}}{n + 1} \: dx_{99}...dx_{1} }[/tex]
[tex]\small{ \displaystyle\tt = -\sum_{n = 1}^{ \infty \frac{}{} \frac{}{} } \frac{1}{n}\int_{0}^{1} \int_{0} ^{ x_{1}} }[/tex]
[tex]\displaystyle \tt= - \frac{1}{(100)!_{} } \sum_{n = 1}^{ \infty } \frac{(n - 1)!(100)!}{(n + 101)!}=−(100)!1n=1∑∞(n+101)!(n−1)!(100)![/tex]
[tex]\displaystyle \tt= - \frac{1}{(100)!_{} } \sum_{n = 1}^{ \infty} \int_{0}^{1} {x}^{n - 1} (1 - x {)}^{100} [/tex]
[tex]\displaystyle \sf - \dfrac{1}{(100!)} \int_{0}^{1} \dfrac{(1 - x)^{100} }{1 - x} \:[/tex]
[tex]\displaystyle\tt { = - \frac{1}{(100)!} \int_{0}^{1} {x}^{99} \: dx=−(100)!1∫01x99dx}
[/tex]
Step-by-step explanation:
[tex]{ \pink{ \displaystyle\tt \int_{0}^{1} \int_{0} ^{ x_{1}} } \sf \pink\int_{ 0 }^{x_{2}... \int_{ 0 }^{x_{99}}} ln(1 -x_{100} ) dx_{100}... dx_{1}}[/t
︎︎︎︎︎︎︎
Goal 1000 points
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 7 fl oz per minute. How fast was the pipe leaking in gallons per hour? PLLLLLLLLLLLLZZZZZZZZZZZ
Answer:
It leaks 420 gallons per hour.
Step-by-step explanation:
7g/m
?/h
7/1 = x/60
(Cross Multiplication)
7 × 60 = x × 1
420 = x
It leaks 420 gallons per hour.
Answer:
3.28 gallons per hour
Step-by-step explanation:
Given that the pipe is leaking at a rate of 7 fluid ounce per minute, and that we need to determine the equivalent leaking rate in gallons per hour. It is important to establish the necessary conversion rates of fluid ounces (fl oz) to gallons (gal), and minutes to an hour.
Conversion rate for fluid ounces (fl oz) to 1 gallon (gal): 128 fl oz = 1 galConversion rate of minutes to hour: 60 minutes = 1 hour.Now that we have established the conversion rates, we can set up the following mathematical operations that will allow us to convert the leaking rate from fluid ounces per minute, to gallons per hour. We can express the conversion process in fraction form:
[tex](\frac{7 fl. oz.}{min})[/tex] × [tex](\frac{1 gal}{128 fl. oz.})[/tex] × [tex](\frac{60 min}{1 hr})[/tex]
Start by multiplying the first two fractions together:
[tex](\frac{7 fl. oz.}{min})[/tex] × [tex](\frac{1 gal}{128 fl. oz.})[/tex] = 0.546875 gallons per minute, or 0.546875 gal/min
Next, multiply 0.546875 gal/min by 60 min/hr. This cancels out the "minute" as a unit of measurement, leaving you with gal/hr.
[tex](\frac{0.546875 gal}{min})[/tex] × [tex](\frac{60 min}{1 hr})[/tex] = 3.28125 gallons per hour, or 3.28 gal/hr.
Therefore, the pipe is leaking at a rate of 3.28 gallons per hour.
Differentiate the function
Answer:
[tex]-\frac{9}{r^4}[/tex]
Step-by-step explanation:
Using Power rule
[tex]\frac{d}{dr} (r^n)=nr^{n-1}\\-\frac{9}{r^4}[/tex]
The answer is F'(r) = [tex]\mathrm {-\frac{9}{r^{4}}}[/tex].
We can rewrite the function as :
F(r) = 3r⁻³
Now, differentiate by power rule :
F'(r) = (-3)3r⁻³⁻¹
F'(r) = -9r⁻⁴
F'(r) = -9/r⁴
Domain:
Range:
HELP I BEG
Ivy bought a bike for $67.82. The sales tax was $4.79. How much money did Ivy spend on the bike before taxes?
Answer: $63.03
Step-by-step explanation:
$67.82 - $4.79 = 63.03
1. Identify the place value for the following: 162.891
Answer:
Hundreds : 1
Tens : 6
Ones : 2
.
Tenths : 8
Hundredths : 9
Thousandths : 1
hint: 180 *
1. Find the missing angle.
29
R
61
T
Answer:
∠ R = 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , that is
∠ R + ∠ S + ∠ T = 180° , substitute values
∠ R + 29° + 61° = 180°
∠ R + 90° = 180° ( subtract 90° from both sides )
∠ R = 90°
a. What is the probability that this couple spends 45 dollars or more?
b. Suppose that the restaurant is currently running a promotion with a 10% discount if the total amount spent by a table is 45 dollars or more. What is expected total amount the couple actually has to pay?
Using the probability table, it is found that:
a) There is a 0.25 = 25% probability that this couple spends 45 dollars or more. b) The expected amount the couple actually has to pay is $36.85.Item a:
To find the probabilities involving the total cost, we have to add the variables X and Y from the table, then:
[tex]P(X = 30) = P(X = 15|Y = 15) = 0.2[/tex]
[tex]P(X = 35) = P(X = 15|Y = 20) + P(X = 20|Y = 15) = 0.15 + 0.15 = 0.3[/tex]
[tex]P(X = 40) = P(X = 15|Y = 25) + P(X = 20|Y = 20) + P(X = 25|Y = 15) = 0.05 + 0.15 + 0.05 = 0.25[/tex]
[tex]P(X = 45) = P(X = 20|Y = 25) + P(X = 25|Y = 20) = 0.1 + 0.1 = 0.2[/tex]
[tex]P(X = 50) = P(X = 25|Y = 25) = 0.05[/tex]
The probability involving values of 45 or more is:
[tex]P(X \geq 45) = P(X = 45) + P(X = 50) = 0.2 + 0.05 = 0.25[/tex]
0.25 = 25% probability that this couple spends 45 dollars or more.
Item b:
For a discrete distribution, the expected value is the sum of each outcome multiplied by it's respective probability, hence, involving the 10% discount for prices above $45:
[tex]E(X) = 0.2(30) + 0.3(35) + 0.25(40) + 0.9[0.2(45) + 0.05(50)] = 36.85[/tex]
The expected amount the couple actually has to pay is $36.85
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To get in shape for the upcoming track season two brothers, Scott and Brian, begin running home after school. Scott runs at a rate of 6 mph and Brian runs at a rate of 4 mph. If they leave school at the same time, Scott arrives home a half-hour before Brian. How long does it take Brian to get home from school
It takes Brian 1.5 hours to get home from school
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let d represent the distance from their school to the house and t represent the time (hours) it takes Brian to teach home.
For Brian:
4 = d/t
d = 4t
For Scott:
6 = d / (t - 1/2)
d = 6t - 3
4t = 6t - 3
2t = 3
t = 1.5 hours
Therefore it takes Brian 1.5 hours to get home from school
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