Answer:
4/5 of the students would have protractors.
Step-by-step explanation:
evaluate the expression: 7 - 3 + 9 x 8 ÷ 2
Answer:
40
Step-by-step explanation:
7 - 3 + 9 x 8 / 2
Multiplication and division left - right.
7 - 3 + 72 / 2
7 - 3 + 36
Add and subtract left to right.
4 + 36 = 40
Which number has a repeating decimal form?
A. sqrt{15
B. 11/25
C. 3/20
D. 2/6
Answer:
D It repeats
Step-by-step explanation:
square root of 15 is 3.87298334621
11/25= 0.44
3/20=.6
D = 0.33333333333
Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Answer:
d. 9
Step-by-step explanation:
y= 0.22x^2 - 1.76x +4.75
x is the time in months so we should replace x by 10
y = 0.22 (10)^2 - 1.76(10) + 4.75
0.22 (100) - 17.6 + 4.75
22 - 17.6 + 4.75
9.15
So the number of laptops that will be sold during month 10 is 9. (you can't have 0.15 of a computer)
Answer:
d. 9
Step-by-step explanation:
The equation: y = 0.22x^2 - 1.76x + 4.75
x: Time in months
y: Number of laptops sold
Since we need to predict the number of laptops that will be sold during month 10, we can replace the x with 10.
The new equation will be: y = 22 - 17.6 + 4.75
Then y will be 9.15
Since there cannot be 0.15 of a laptop, we round the number 9.15 to a whole number, which is 9.
D) 9 is our final answer to this question.
Match the scenarios to their corresponding boundaries.
The correct choices based on the integers are: 1a, 2b, 3d, and 4c.
In the question, we are asked to match the scenarios to their corresponding boundaries.
miles traveled by a car in one hour: this can be non-negative numbers as the distance traveled by a car cannot be negative, but it is not infinitely possible, making the right option a. numbers between 0 and 70.average Celsius temperature in Antarctica: is mostly negative, and even if positive, very low. making the right option b. numbers between -100 and 20.amount of money owed on a car: this can be any non negative number without limit, making the right option d. no negative numbers.age when a baby takes their first step: as its an age it wont be a negative number, and its a baby age so it will be very small, making the right option, c. no negative numbers and positive numbers less that 2.Thus, the correct choices based on the integers are: 1a, 2b, 3d, and 4c.
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Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday
ii,Solve the equation above
On a coordinate plane, triangle D E F has points (negative 8, 8), (10, negative 2), and (negative 8, negative 8).
Find the area of the triangle DEF.
Area = square units
Answer: 144
Step-by-step explanation:
The length of DF is 16.
The horizontal distance from DF to E is 18.
So, the area is [tex]\frac{1}{2}(16)(18)=144[/tex]
The area of the triangle DEF is approximately equal to 144.014 square units.
How to find the area of a triangle by Heron's formulaTriangles can be generated on a Cartesian plane by marking three non-colinear points on there. Heron's formula offers the possibility of calculating the area of a triangle by only using the lengths of its three sides, whose formula is now introduced:
A = √ [s · (s - DE) · (s - EF) · (s - DF)] (1)
s = (DE + EF + DF) / 2 (2)
Where s is the semiperimeter of the triangle.
First, we determine the lengths of the sides DE, EF and DF by Pythagorean theorem:
Side DE
DE = √ [[10 - (- 8)]² + (- 2 - 8)²]
DE ≈ 20.591
Side EF
EF = √ [(- 8 - 10)² + [- 8 - (- 2)]²]
EF ≈ 18.974
Side DF
DF = √[[- 8 - (- 8)]² + (- 8 - 8)²]
DF = 16
Then, the area of the triangle DEF is by Heron's formula:
s = (16 + 18.974 + 20.591) / 2
s = 27.783
A = √[27.783 · (27.783 - 20.591) · (27.783 - 18.974) · (27.783 - 16)]
A ≈ 144.014
The area of the triangle DEF is approximately equal to 144.014 square units.
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Hey can someone help me with this?
Answer:
Step-by-step explanation:
A. a = $1350 b. b= 89%
B. 1350(.89)^t = 675
t = 5.9 years
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Using the binomial distribution, we have that you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 0.2308, as of the 52 cards, there are 12 faces, hence 12/52 = 0.2308.Then the expected value is found as follows:
E(X) = np = 35 x 0.2308 = 8
You would expected to draw a face card 8 times.
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The ratio of the triangle are in the ratio 1:2:3 Find the angles of this triangle?
Answer:
Step-by-step explanation:
let we suppose the ratios as x , 2x and 3x
we know that,
x + 2x + 3x = -----
6x= -------
x= -----/6
therefore x = ......
2x = 2 * x (value of x)
3x = 3 * x (value of x)
and the question is solved
Answer:
let the ratio be 1x,2x,3x
Now,
1x+2x+3x=180°(sum of angles of triangle are 180)
or,6x=180°
or,x=180/6
or,x=30°
Then,
1x=1*30
=30°
2x=2*30
=60°
3x=3*30
=90°
Point P is on line segment \overline{OQ}
OQ
. Given PQ=x+7,PQ=x+7, OP=4x-10,OP=4x−10, and OQ=4x,OQ=4x, determine the numerical length of \overline{OQ}.
OQ
.
Answer:
Step-by-step explanation:
4x - 10 + x + 7 = 4x
5x - 3 = 4x
-3 = -x
x = 3
4(3) - 10 = 12 - 10 = 2
3 + 7 = 10
10+2 = 12
4(3)= 12
distance between −42 and −78
Answer:
36 units
Step-by-step explanation:
to find the distance take the absolute value of the difference, that is
| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36
or
| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36
Answer:
-36
Step-by-step explanation:
-78 - (-42)
= -78 + 42
= -36
50 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 31 pupils use the swimming pool. 28 pupils use the gym. 7 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
Using it's concept, it is found that there is a 0.3 = 30% probability to select a pupil that uses the swimming pool but not the gym.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that 50 - 7 = 43 pupils use at least one of the pool or the gym.
We use the following relation, considering the numbers of each:
Both = Pool + Gym - At least one
Hence:
Both = 31 + 28 - 43 = 16.
From this, we have that out of 50 pupils, there are 31 - 16 = 15 pupils who use the pool but not the gym, hence the probability is:
p = 15/50 = 0.3 = 30%.
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g(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
By evaluating the function, we conclude that f(10) = -7
How to evaluate the function f(x)?
Here we know that:
g(x) = 2x - 8
And f(x) = 5 - g(x).
Then we can write:
f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13
Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.
f(10) = -2*10 + 13 = -20 + 13 = -7
Then, we conclude that f(10) = 7
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Under his cell phone plan, christopher pays a flat cost of $59 per month and $3 per gigabyte. he wants to keep his bill at $62.90 per month. how many gigabytes of data can he use while staying within his budget?
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
How many gigabytes of data can he utilize while staying within his budget?The number of gigabytes of data that Christopher can use while staying within his budget is 1.8 gigabytes.
Based on the information, we get
59 + (3 × g) = 62.90
59 + 3g = 62.90
simplifying the equation, we get
3g = 62.90 - 59
3g = 3.9
Divide both sides by 3, and we get
3g/3 = 3.9/3
g = 1.3
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
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How many liters of water should be added to 18 liters of a 14% bleach solution so that the resulting solution contains only 10% bleach? original (l) added (l) new (l) amount of bleach 2.52 0 amount of solution 18 x 1.8 liters 7.2 liters 15.5 liters 25.2 liters
18 liters of 14% bleach contains 0.14×18 = 2.52 liters of bleach.
Adding [tex]x[/tex] liters of pure water to the solution increases the total volume to [tex]18+x[/tex] liters without changing the total amount of bleach.
To end up with a 10% bleach solution, we must add
[tex]\dfrac{2.52}{18+x} = 0.10 \implies 2.52 = 1.8 + 0.10x \implies 0.10x = 0.72 \implies x=\boxed{7.2}[/tex]
liters of water.
Answer:
b
Step-by-step explanation:
Translate the sentence into an equation.
15 less than Taryn's age is 20
use the variable a to represent Taryn's age.
answer choices:
a. 20-a = 15
b. 15-a = 20
c. a-15= 20
d. 20-15 = a
Answer: c. a-15= 20
Step-by-step explanation:
The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20
The volume of a cone is 1,782 cubic centimeters. a cylinder has the same radius and height as the cone. what is the volume of the cylinder?
The volume of the cylinder that has same height and radius with the given cone is 5,346 cm³
What are the 3-D figure?Pyramids and prisms are examples of three-dimensional shapes, as are shapes with curved surfaces. The three-dimensional prism shape has two bases that are parallel and congruent. Any polygon is acceptable for the bases, which are two of the faces. Rectangles make up the remaining faces.
What is the Volume of a Cylinder?Given that the cylinder and the cone have the same radius and height, the volume of a cylinder equals 3 times the volume of a cone.
According to the given figure:
Given, a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder,
therefore,
Volume of the cylinder = 3 x (1,782)
Volume of the cylinder = 5,346 cubic centimeters
Hence, the volume of the cylinder is 5,346 cubic centimeter.
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Use the diagram to answer each part of the question. The image is not drawn to scale.
will mark brainiest if corrects. try ur best!
In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
The height of the tree and the building are 7.6 m and 28.6 m respectively.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Triangle BGD, CHD and AFD are similar triangles.
CH = 1.6, DH = 8, GH = 30, GF = 105
FH = GF + GH = 105 + 30 = 135
FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38
Hence, using similar triangles:
BG/CH = GD / DH
BG / 1.6 = 38/8
BG = 7.6 m
Also:
building/CH = DF / DH
building / 1.6 = 143/8
building = 28.6 m
The height of the tree and the building are 7.6 m and 28.6 m respectively.
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Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x² + 2
a = 0
b= 6
6 intervals
Answer:
67 square units
Step-by-step explanation:
The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.
AreaThe attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.
The approximate area is 67 square units.
Split up the interval [0, 6] into 6 equally spaced subintervals of length [tex]\Delta x = \frac{6-0}6 = 1[/tex]. So we have the partition
[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]
where the left endpoint of the [tex]i[/tex]-th interval is
[tex]\ell_i = i - 1[/tex]
with [tex]i\in\{1,2,3,4,5,6\}[/tex].
The area under [tex]f(x)=x^2+2[/tex] on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,
[tex]\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}[/tex]
where we use the well-known sums,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Sketch The Graphs:
y = -1/3x -2
Answer:
Step-by-step explanation:
The graph of the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted. The graph is shown below.
A straight line is of the form y = mx + c, where m is the slope and c is the y-intercept.
To plot the given straight line [tex]y = -\frac{1}{3}x -2[/tex], follow the following steps:
Step 1: Substitute x = 0 in the given equation to obtain the point where the line intersects the y-axis.
y = 0 - 2
y = -2
The point at the y-axis is (0, -2).
Step 2: Substitute y = 0 in the given equation to obtain the point where the line intersects the x-axis.
[tex]0 = -\frac{1}{3}x -2\\x = -6[/tex]
The point at the x-axis is (-6, 0).
Step 3: Draw a straight line passing through both points.
Thus, the straight line [tex]y = -\frac{1}{3}x -2[/tex] is plotted.
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pipe A can fill a tank in 3 hours. if pipe B can fill the same tank in 2 hours, how many minutes will it take both pipes to fill 2/3 of the tank
Answer:
pipe A =3. pipe B=2 find LCM of 3 and 2 . it will be 6 . Then take 6×2/3 it will give you 4 minutes as the answerAnswer:
48 minutes
Step-by-step explanation:
The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.
Sum of ratesThe sum of the filling rates is ...
rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour
Fill timeThe time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:
time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour
There are 60 minutes in an hour, so the fill time is ...
(4/5 hour)×(60 min/hour) = 48 min
It will take 48 minutes for both pipes to fill 2/3 of the tank.
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
The number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
Simultaneous equationSimultaneous equation is an equation which involves the solving for two unknown values at the same time.
number of contemporary titles = xnumber of classic titles = yx + y = 3,500
x – y = 2,342
Add both be equation
x + x = 3,500 + 2,342
2x = 5,842
x = 5,842 ÷ 2
x = 2,921
Substitute x = 2,921 into
x – y = 2,342
2,921 - y = 2, 342
-y = 2,342 - 2,921
-y = -579
y = 579
Therefore, the number of contemporary titles and classic titles in Jarred DVDs collection is 2,921 and 579 respectively.
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Lois made a dish with61/3 cups of pasta. One serving of the pasta is 0.2 cups. How many servings of pasta were in the dish Lois made?
A.
B.
C.
D.
The number of servings of pasta were in the dish Lois made is 31.67.
Unit valueNumber of cups of pasta Lois made = 6 1/3 cupsA serving of the pasta = 0.2 cupsNumber of servings of pasta were in the dish Lois made = Number of cups of pasta Lois made / A serving of the pasta
= 6 1/3 ÷ 0.2
= 19/3 ÷ 0.2
= 19/3 × 1/0.2
= (19×1) / (3 × 0.2)
= 19/0.6
= 31.6666666666666
Approximately,
Number of servings of pasta were in the dish Lois made is 31.67 servings
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Jason solved the following equation to find the value for x.
-8.5x-3.5x=-78
X=6.5
Describe how Jason can check his answer.
Chris, nina, and iana each have a 3/4 chance of going to cafe shirley for an afternoon coffee at 1:00pm. jeffrey will only go to cafe shirley for a coffee if at least one of his friends is at the cafe. what is the probability that jeffrey goes to cafe shirley for a coffee today?
Answer:
Jeffrey has 225 % chance to go to Cafe Shirley.
Step-by-step explanation:
given,
chance of going to Cafe
Chris = 3/4
Nina =3/4
iana = 3/4
To find the total probability you should add all of them:
Total probability= 3/4 + 3/4 + 3/4
= 9/4 = 2.25
to convert to percent you should times 100
2.25 x 100 = 225%//
Complete the proofs, ASAP!!! (Geometry)
1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)
2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)
3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)
4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)
5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)
6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)
Solve the given differential equation by undetermined coefficients. y'' 4y' 4y = 2x 3
The solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
According to the given question.
We have a differential equation
[tex]y^{"} + 4y^{'} + 4y = 2x^{3}[/tex]
The above differerntial equation acn be written as
[tex](D^{2} +4D+ 4)= 2x^{3}[/tex]
Now, the auxillary equation for the above differential equation is given by
[tex]m^{2} + 4m + 4 = 0[/tex]
[tex]\implies m^{2} + 2m + 2m + 4 = 0[/tex]
⇒ m (m + 2) + 2(m + 2) = 0
⇒ m(m + 2)(m + 2) = 0
Therefore,
[tex]C.F = (C_{1} + C_{2}x)e^{-2x}[/tex]
Now,
[tex]PI = \frac{1}{D^{2} +4D+4} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}[/tex]
[tex]\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}[/tex]
[tex]\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6][/tex]
[tex]\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Therefore, the solution of the differential equation will be
y = CI + PI
[tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]
Hence, the solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .
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I'm thinking of a number. If I add 4 to the number and then multiply the result by 3,the answer is the same as subtracting 5 from the number and then multiplying the result by 2.
(a) in terms of x?
(b) solve the equation n find the number what I'm thinking of
Answer:
x=-22
Step-by-step explanation:
Let's substitute the number you are thinking of with x
(x+4)*3=(x-5)*2
3x+12=2x-10
x+12=-10
x=-22
A pedestal for a statue is made with 405 cubic feet of concrete. a rectangular prism with a height of 9 feet. what is the area of the base of the pedestal? 6.7 square feet 22.5 square feet 45 square feet 3,645 square feet
45 square feet is the area of the base of the pedestal.
what is rectangular prism?
A rectangular prism is a 3D figure with 6 rectangular faces. To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.we know that
The volume of the pedestal (rectangular prism) is given by the formula
V = B × h
where
B is the area of the rectangular base of pedestal
V = 405 ft³
h = 9 ft
put the given values in the formula and solve for B
405 = B × 9
B = 405/9
B = 45 ft²
Therefore, 45 square feet is the area of the base of the pedestal.
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A diver is standing on a spring board 48 feet above the pool. She jumps from the platform with an
initial upward velocity of 8 feet /second. Use the formula d(t)= -16(2t - 3)(t+1), where d is the
height of the diver above the water and t is the time in seconds. How long will it take for her to hit
the water?
It will take the diver 1.5seconds for her to hit the water
Linear equationsLinear equations are equation that has a leading degree of 2. Given the expression that expresses the distance covered by the diver as a function of time as shown;
d(t)= -16(2t - 3)(t+1)
where;
d is the height of the diver above the water and;
t is the time in seconds.
Given the following
d = 0 (the distance on the ground)
Substitute into the formula below;
-16(2t - 3)(t+1)= 0
Divide through by -16
(2t - 3)(t+1) = 0
Determine the time
2t - 3 = 0
t = 3/2
Similarly;
t +1 = 0
t = -1
Hence it will take the diver 1.5seconds for her to hit the water
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