Answer:
y = -3/2x+3
Step-by-step explanation:
We first need to find the slope using
m = (y2-y1)/(x2-x1)
= (9-0)/(-4 -2)
9/-6
=-3/2
We will use the slope intercept form of the equation
y = mx+b where m is the slope and b is the y intercept
y = -3/2x+b
Substitute a point into the equation
0 = -3/2(2) +b
0 = -3+b
b = 3
y = -3/2x+3
if you flip a coin 6 times , about how many times would you expect to flip heads or tails?
What is the slope of the line that passes through the points (0,-7) and (-4,3)
Answer:
Step-by-step explanation:
To find slope you have to take y2-y1 over x2-x1
y2=your second y poiny
y1=first y point
x2=second x point
x1=first x point
Since it is minus a negative you get to change it to a plus sign, because they cancel each other out.
3 + 7
____
-4-0
10/-4
This isn't quite simplified, so you find a common factor for the numerator (top number) and the denominator (bottom number). You should note the number has to go into both numbers, not just one. The largest common factor would be 2 in this case.
10/2=5
-4/2=-2
Now your simplified answer would be 5/2
The slope of the line will be "[tex]-\frac{5}{2}[/tex]".
The given points are:
[tex](x_1, y_1) = (0,-7)[/tex][tex](x_2, y_2)= (-4,3)[/tex]The slope (m) will be:
= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the given values, we get
= [tex]\frac{3-(-7)}{-4-0}[/tex]
= [tex]\frac{3+7}{-4}[/tex]
= [tex]-\frac{10}{4}[/tex]
= [tex]-\frac{5}{2}[/tex]
Thus the above slope is right.
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What's the answer to this equation .......
3= x÷2-1
Answer:
x=8
Step-by-step explanation:
If you subtract 3 from both sides then subtract -x/2 from both sides your equation should be simplified down to
-x/2 = -4. if you multiply the 2 on both sides the equation is -x=-8. but now you have to divide by negative 1 on both sides and you get x=8
PLEASE HELP!!!!!The volume of a cube is represented by the expression below, where s is the side length of the cube.
s to the power of 3
Find the volume of a plastic cube building block with a side length of 6 centimeters.
A.
72 cubic centimeters
B.
128 cubic centimeters
C.
240 cubic centimeters
D.
216 cubic centimeters
Answer:
D. 216 cubic centimetres.
Step-by-step explanation:
The answer is D, because 6 to the 3rd power is 216. therefore, if the side length is 6, the answer is 216.
(4x+3)(2x-5)
Help please 10 points
Answer:
Step-by-step explanation:
hello :
(4x+3)(2x-5)=0
4x+3=0 or 2x-5=0
x= -3/4 or x=5/2
(4x+3)(2x-5) = 8x²-14x-15
Step-by-step explanation:
Given,
(4x+3)(2x-5)
To find the value of the given multiplication.
Formula
(a+b)(c+d)
= a(c+d)+b(c+d) = ac+ad+bc+bd
Now,
(4x+3)(2x-5)
= 4x(2x-5)+3(2x-5)
= 8x²-20x+6x-15
= 8x²-14x-15
In a right triangle, the length of one leg is 7 ft. The length of the other leg is 10 ft. What is the length of the hypotenuse?
Final answer:
To find the length of the hypotenuse in a right triangle with legs of 7 ft and 10 ft, we use the Pythagorean theorem, resulting in a hypotenuse of approximately 12.21 feet.
Explanation:
The student is asking about the length of the hypotenuse in a right triangle where one leg is 7 ft and the other is 10 ft. To find the hypotenuse, we use the Pythagorean theorem which states a² + b² = c², where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.
For this triangle, the calculations would be:
a² = 7² = 49
b² = 10² = 100
a² + b² = c²
49 + 100 = c²
149 = c²
c = [tex]\sqrt{149[/tex]
c = 12.21 ft (rounded to two decimal places)
Therefore, the length of the hypotenuse of the triangle is approximately 12.21 feet.
Currently, you have made a
75, 83, and a 78 on your tests in
math. What do you need to
make on the next test in order to
get an average of an 80?
Answer:
84
Step-by-step explanation:
4 test grades with an average of 80 would have a total of 80x4=320.
75+83+78=236
320-236=84
Hard please help. :/
Answer:58
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
since it equals to 90 you subtract that with 32
which gives you 58
a cone has a radius of 2.5 and a height of 10 what is the volume
Answer:
V= pi.r².h/3
=22/7×2.5²×10/3
=65.47
Step-by-step explanation:
Raquel and Van live in two different cities. As a part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data show mean = 3.42 and standard deviation = 0.07. Van’s data show mean = 3.78 and standard deviation = 0.23.
Which statement is true about their gas-price data?
A: Raquel’s data are more likely closer to $3.42 than Van’s data are to $3.78.
B: Van’s data are more likely closer to $3.42 than Raquel’s are to $3.78.
C: Raquel’s data are more likely closer to $3.78 than Van’s data are to $3.42.
D: Van’s data are more likely closer to $3.78 than Raquel’s are to $3.42.
Answer:
A: Raquel’s data are more likely closer to $3.42 than Van’s data are to $3.78
Step-by-step explanation:
Given that Raquel’s standard deviation is less than Van's standard deviation, then Raquel’s data are more likely closer to Raquel’s mean than Van’s data are to Van's mean.
Answer:
A
Step-by-step explanation:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer: Zero
Step-by-step explanation:
A negative slope is a linear line that is sloped from the upper left to the bottem right. A positive is the oppisate and an undefined line is vertical. A zero line is horizontal.
The word describes the slope of the line is zero
What is slope of a line?The slope of the line is defined as its inclination towards the x axis.
How to know which word describes the slope of the line?In the given figure,
The line is parallel to the x axis.So, angle between the line and the x-axis is 0 that is the line is totally inclined towards the x axis.So, the slope will be zero
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But these are graphs, not numbers! What do you think Diego and Mai are thinking?
Answer:
Diego and Mai are thinking of the slopes of the graphs!
Step-by-step explanation:
The slopes of the graphs are as follows:
Right: Negative slope
Center: Zero slope
Left: Positive slope
Therefore, you can conclude that the graphs are organized in order of slope.
(Let me know if you need more explanation as to why we know the slopes are positive, negative, zero, etc.)
h(x)=x-4 what’s is the domain of h?
Answer:
all real number
Step-by-step explanation:
since h(x) is polynomial function
Final answer:
The domain of the function h(x)=x-4 is all real numbers, as there are no restrictions on the value of x.
Explanation:
The domain of a function represents all the possible values that can be input into the function. For the function h(x)=x-4, there are no restrictions on the value of x, since x represents a real number and there are no denominators or square roots to consider.
Therefore, the function h(x)=x-4 is defined for all real numbers, making the domain of h to be all real numbers, which is often denoted by the symbol (-∞, +∞) or simply written as 'all real numbers'.
Cooper and his children went into a bakery and where they sell cupcakes for $2.50 each and donuts for $1.50 each. Cooper has $40 to spend and must buy a minimum of 18 cupcakes and donuts altogether. If Cooper decided to buy 7 cupcakes, determine the maximum number of donuts that he could buy.
Answer:15
15
7 cupcakes=17.5
40-17.5=22.5
donuts are 1.50
22.5 divided by 1.5 is 15
The maximum number of donuts Cooper can buy is 15.
Given that, the cost of cupcakes = $2.50 and the cost of donuts = $1.50.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let the number of cupcakes be x and the number of donuts be y.
Cooper wans to buy a minimum of 18 cupcakes and donuts altogether
That is, x+y≥18
Cooper has $40 to spend on cupcakes and donuts.
So, 2.50x+1.50y≤40
Cooper decided to buy 7 cupcakes
Then number of donuts will be
2.50(7)+1.50y≤40
⇒17.5+1.50y≤40
Subtract 17.5 on both the sides of a inequality, we get
17.5+1.50y-17.50≤40-17.50
⇒1.50y≤22.5
Divide 1.50 on both the sides of a inequality, we get
1.50y/1.50≤22.5/1.50
⇒y≤15
Therefore, the maximum number of donuts Cooper can buy is 15.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 11 people took the trip. She was
able to purchase coach tickets for $330 and first class tickets for $1110. She used her total budget for airfare for the trip, which was $8310. How many first class
tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought
Answer: 8 First class tickets
Step-by-step explanation:
You can set up a system of equations for this problem. Let x = number of coach tickets and y = number of first class tickets. Then:
330x + 1220y = 12730 (cost of coach tickets plus cost of first class tickets is total budget)
x + y = 17 (number of coach tickets plus number of first class tickets is total number of people)
Solve the second equation for y to get y = 17 - x, then plug that into the first equation and solve for x:
330x + 1220(17 - x) = 12730
330x + 20740 - 1220x = 12730
-890x + 20740 = 12730
-890x = -8010
x = 9
Sarah bought x = 9 coach tickets. Plug that into the second equation and solve for y:
9 + y = 17
y = 8
Sarah bought y = 8 first class tickets.
Answer:
6 first class 5 coach
Step-by-step explanation:
msg me if you need me to explain it
I
2/
18
s 0
15th
15th
so
If you choose from the following M&M colors, what
is the probability that you choose blue?
5 green
6 yellow
8 blue
Answer:
8/19
Step-by-step explanation:
Total = 5 + 6 + 8 = 19
P(blue) = 8/19
Or 0.4210526316
Meters and centimeters are units of length in the metric system. True or False?
Answer:
True
Step-by-step explanation:
Meters, centimeters, inches, miles, etc. are units of length.
Triangle C F E is shown. Angle C F E is a right angle. An altitude is drawn from point F to point D on side C E, forming a right angle. The length of F D is 9, the length of C D is 5, and the length of D E is 2 x + 3.
What is the value of x and the length of segment DE?
StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)
x =
Length of = units
What is the value of x and the length of segment DE?
StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)
Answer: Keep it simple
x =
6.6
Length of =
16.2
units
The value of x and one of the sides of the triangle are needed.
[tex]x=6.6\ \text{units}[/tex]
[tex]DE=16.2\ \text{units}[/tex]
[tex]CD=5\ \text{units}[/tex]
[tex]FD=9\ \text{units}[/tex]
[tex]DE=2x+3[/tex]
Finding CF
[tex]CF^2=CD^2+FD^2\\\Rightarrow CF^2=106\ \text{units}[/tex]
In triangle DEF
[tex]FE^2=DE^2+DF^2\\\Rightarrow FE^2=(2x+3)^2+81[/tex]
In triangle CFE
[tex]CE^2=CF^2+FE^2\\\Rightarrow (5+2x+3)^2=106+(2x+3)^2+81\\\Rightarrow (8+2x)^2=187+(2x+3)^2\\\Rightarrow 64+4x^2+32x=187+4x^2+9+12x\\\Rightarrow x=\dfrac{187-64+9}{32-12}\\\Rightarrow x=6.6\ \text{units}[/tex]
[tex]DE=2x+3=2\times 6.6+3\\\Rightarrow DE=16.2\ \text{units}[/tex]
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i need help for this equation x-2y=6
Answer:
y=1/2-3
Step-by-step explanation:
x-2y=6
-2y=-x+6
y=1/2-3
or
-2y=6
y=-3
x=6
Select the correct answer.
Solve for p.
2p - 29 over 4 = 4
what is the answer?
PLATO
=(2p - 29)/4= 4
=2p - 29 = 16
=2p = 16+29
=2p = 45
=p= 45/2
= p=22.5
Hope this will help u mate :)
Answer:
p=22.5
Step-by-step explanation:
A box is known to hold exactly 125 in3. Which side dimensions produce the most accurate measurement of the box?
A)
4.9 x 5.1 x 5.0
B)
4.91 x 5.11 x 5.01
C)
4.911 x 5.112 x 5.011
D)
4.9112 x 5.1122 x 5.0114v
Answer:
A.4.9 x 5.1 x 5.0
Step-by-step explanation:
The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B cm2. Which expressions show the area of the shaded region in terms of A and B? Check all that apply.
4A + B
8A + B
2A + B
1.5B
12A
Answer:
The correct answers are 4A+B, 1.5B, 12A
Step-by-step explanation:
The area of the whole figure is 4A+B cm²
What is an area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The space enclosed by the boundary of a plane figure is called its area.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
Given that, a figure having the area of one of the small right triangles outlined in blue is A cm² while the area of the square outlined in red is B cm²
The total area = the sum of the area of the 4 triangles and the square,
= A + A + A + A + B = 4A + b
Hence, the area of the whole figure is 4A+B cm²
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The complete question is attached
Construct a 95% confidence interval for the population mean, mu. Assume the population has a normal distribution. A random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours. Round to the nearest tenth.
Given Information:
Number of lithium batteries = n = 16
Mean life of lithium batteries = μ = 645 hours
Standard deviation of lithium batteries = σ = 31 hours
Confidence level = 95%
Required Information:
Confidence Interval = ?
Answer:
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Step-by-step explanation:
The confidence interval is given by
[tex]CI = \mu \pm t_{\alpha/2} (\frac{\sigma}{\sqrt{n}})[/tex]
Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of
tα/2 = (1 - 0.95) = 0.05/2 = 0.025
and the degree of freedom is
DoF = n - 1 = 16 - 1 = 15
The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)
[tex]CI = 645 \pm 2.131(\frac{31}{\sqrt{16}})[/tex]
[tex]CI = 645 \pm 2.131(7.75})[/tex]
[tex]CI = 645 \pm 16.515[/tex]
[tex]CI = 645 - 16.515 \: and \: 645 + 16.515[/tex]
[tex]CI = 628.5 \: to \: 661.5 \: hours[/tex]
Therefore, the 95% confidence interval is 628.5 to 661.5 hours
What does it mean?
It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)
Which expression is equivalent to 7 b + 4 b minus 1 b?
A. 2b
B. 4b
C. 10b
D. 12b
Answer:
c
Step-by-step explanation:
Answer:
ITS CStep-by-step explanation:
10bIn the equation (x-3)2+(4+4)2=121, the radius of the circle is
Answer: The radius of the circle in 11
Final answer:
The equation is in the standard form (x - h)² + (y - k)² = r², where r is the radius. Thus, the square root of the constant term 121 would give the radius, which is 11.
Explanation:
To find the radius from an equation of a circle in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is the radius, we need to compare it to the given equation.
As per the standard form, the number on the right side of the equation is r², the square of the radius.
We have (x - 3)² + (4 + 4)² = 121, which can be written as (x - 3)² + (8 - 0)² = 121, considering (3,0) as the center of the circle, the radius would be the square root of 121, which is 11.
Elisha wants to draw a triangle. She starts by drawing a line 15 centimeters long and two angles, 80° and 55°. What will the third angle measure?
A) 45°
B) 55°
C) 70°
D) 80°
A. 45 is your answer
The third angle is 45°.
Option A is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The two angles in the triangle are 80 and 55.
Now,
The sum of all the angles in the triangle is 180.
Third angle = x
So,
80 + 55 + x = 180
135 + x = 180
Subtract 135 on both sides.
x = 180 - 135
x = 45
Thus,
The third angle is 45°.
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A farmer has a square lot that is 200 feet on each side. She has a very powerful sprinkler that sprays water in a circle she doesn’t want to waste any water, so she’ll set her sprinkler so that it doesn’t spray any water outside of her lot. What is the largest percentage of her lot that she can water? (Answer to the nearest percent)
Answer:
78.5%
Step-by-step explanation:
Area of a 100ft radius circle = 628sqm
Area of rectangle = 800sqm
= 172sqm difference in size
if 800 sqm = 100%
Then 600 sqm = 3/4 = 75%
60sqm =3/40 = 7.5%
6sq m =3/400 =0.75%
2 sq m = 0.25%
30sqm = 1/2 of 7.5%= 3.75
3.75-0.25 = 3.50%
3.50% + 75 = 78.5%
Which description matches the function represented by the values in this
table?
1
2
3
972
324
108
36
12
O A. exponential decay
O B. exponential growth
O
C. linear growth
O
D. linear decay
Answer:
Exponential Decay
Step-by-step explanation:
The description that matches the function represented by the values is A. exponential decay.
What is exponential growth or decay function?Consider the function: [tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is plus sign, so there is exponential growth happening by r fraction or 100r %
If there is negative sign, so there is exponential decay happening by r fraction or 100r %
The given function is
[tex]y = a(1\pm r)^m\\972 = 1(1\pm r)^m[/tex]
The table shows the exponential decay function.
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in a class there are 8 students who play football and cricket 4 students who do not play football or cricket 14 students who play football 20 students who play cricket find the probability that a student chosen at random plays football or cricket or both
Answer:
Step-by-step explanation:
hello :
here is an solution :
The probability that a student chosen at random plays football or cricket or both is approximately 0.8667, or 86.67%, after considering the number of students playing each sport and accounting for those who play both.
To calculate the probability that a student chosen at random plays football or cricket or both, we can use the concept of probability along with a Venn diagram to organize our information.
First, we need to calculate the total number of students that play at least one of the sports. We know that 8 students play both football and cricket, 14 students play football, and 20 students play cricket. However, the 8 students that play both sports are included in the totals for both football and cricket. Therefore, to find the number of students who play at least one sport, we need to subtract the students counted twice because they play both sports:
Total playing football or cricket or both = (Number playing football) + (Number playing cricket) - (Number playing both)
= 14 + 20 - 8
= 26 students
We also know there are 4 students who do not play football or cricket. To find the total number of students, we add the number of students who play either sport to those who play neither:
Total number of students = 26 (playing sports) + 4 (not playing any sports)
= 30 students
The probability that a student chosen at random plays football or cricket or both is calculated by dividing the number of students who play either sport by the total number of students:
P(playing football or cricket or both) = Number of students playing sports / Total number of students
= 26 / 30
= 0.8667 (rounded to four decimal places)
The probability is approximately 0.8667, or 86.67%.
What is the area of a circle with a diameter of 16.2 in.?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer in the box.
In 2
Answer
206.02
Step-by-step explanation:
r=d/2
=16.2/2=8.1
3.12*8.1*8.1=206.0154
to the nearest hundred=206.02
The area of the circle with a diameter of 16.2 inches is approximately 206.24 square inches.
Explanation:The area of a circle can be found using the formula A = πr^2, where π represents the mathematical constant pi and r is the radius of the circle. Since the diameter of the circle is given as 16.2 inches, we can find the radius by dividing the diameter by 2: r = 16.2 / 2 = 8.1 inches. Now we can plug in this value into the formula to find the area: A = 3.14 * (8.1)^2 = 206.2446 square inches. Rounding this to the nearest hundredth, the area of the circle is approximately 206.24 square inches.
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