Answer:(approx) 6.
Step-by-step explanation:Here μ=51 and σ=15
Z=
σ
X−μ
=
15
X−151
When X=120, Z=
15
120−151
=−2.067
When X=155, Z=
15
155−151
=0.2667
When X=185, Z=
15
185−151
=
15
35
=2.2667
(i) P(120<X<155)=P(−2.07<Z<0.27)
=∫
−2.067
0.2667
ϕ(z)dz=∫
0
0.2667
ϕ(z)dz+∫
0
2.0667
ϕ(z)dz
=0.4803+0.1026=0.5829.
Here N=500
∴ The number of students whose weight is between 120 and 155 pounds is
0.5872×500=291
(ii) P(X<185)=P(Z>2.27)=∫
2.2667
∞
ϕ(z)dz
=∫
0
∞
ϕ(z)dz−∫
0
2.2667
ϕ(z)dz=0.5−0.4881=0.0119
∴ the number of students with weight about 185 pounds.
=0.0119×500= (approx) 6.
Which is the graph of f(x)=3^x
The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.
How to determine the graph associated with a given function
In this question we must compare a given exponential function with a set formed by four functions. As the function is crescent and monotonous, then we can choose the correct graph by a evaluating the function for a given x-value and find the graph that matches with such finding:
f(5) = 3⁵
f(5) = 243
The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.
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Solve (x+7)^2=49 algebra
Answer: x = 0
Step-by-step explanation:
Given:
(x + 7)² = 49
Distribute:
x² + 7² = 49
Square:
x² + 49 = 49
Subtract 49 from both sides of the equation:
x² = 0
x = 0
The only solution to this equation is 0.
-> We can also see this with graphing. See attached.
answer:
x=0
Step-by-step explanation:
(x+7)^2=49
take the square root of both sides
√(x+7)^2=√49
x+7=7
x=0
How much should you invest at 3.7% simple interest in order to earn $70 interest in 11 months?
Step-by-step explanation:
in this condition we are given simple interest time and rate
so principal is missing so we should use the formula of principal that is
P=I×100/T×R
but we should convert that month in to years and we convert it by dividing it by 12.
21 ounce of cat food equally among 4 cats
Answer:
5.25
Step-by-step explanation:
Using multiplication, if you do 4x5 you get 20, so adding .25 to the equation will add 1, therefore 20+1=21
So long story short 4 x 5.25 = 21
5.
In the parallelogram ABCD, the diagonals AC and BD
are equal in length. What is the measure of the angle A
?
two
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
How to solve this?
Answer:
(E) 90°
Step-by-step explanation:
The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.
Any angle of a rectangle is 90°.
_____
Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.
At 1:00 pm, Ryan realizes his computer has been unplugged. He needs to work on the computer in his car and wants it to be fully charged. The image on the right represents the time it took for the laptop to charge.
Resources:
Desmos Guide
Regression tool
Line of Best Fit Video
When can Ryan expect his laptop to be fully charged? Do a quick estimate and explain your reasoning.
He does a quick calculation at 1:17 and estimates the computer charges 1% a minute. He estimates it will be fully charged by 2:30. Was he right?
Was his prediction over or under?
Graph all the data points. Draw an original graph or use a digital graphing calculator. Hint: First, convert the minutes to decimals then create a table of values.
Use the regression tool on Desmos (see the Desmos guide) to graph the points on a line, or draw your own. Write a line of best fit in the form y = mx + b.
Based on the line of best fit, when will the computer be fully charged?
Was your first estimate correct? Why do you think Ryan's first estimate was not accurate?
The amount of time it will take for Ryan expect his laptop to be fully charged by following the example on the image attached.
What is the battery percentage about?16 %= 4m
28%= 15m
37%= 10m
51% = 24m
69% = 34m
81%= 17m
Based on his quick calculation at 1:17 and estimates that it will be fully charged by 2:30 is wrong because when you look at the i]steps above, you will see that it the minute used too charge varies.
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help me slove this please i really need thee answer
4.5,4.316,4.32,4.312 from least to greatest
4.5, 4.316, 4.32, 4.312
= 4.500, 4.316, 4.320, 4.312
Look at the thousandths and hundreths place in the decimal section.
Least to greatest = 4.312 < 4.316 < 4.32 < 4.5
Please answer, thank you. Image below.
I need to find the missing angle. The letter represents the missing angle
Answer:
Top Image: 56°
Bottom Image: 134°
Step-by-step explanation:
I'm not sure which image you have a question on, so I'll just solve both.
Top Image:
We know that the sum of the angles will add up to 180 and that the angles of the triangle are f, f, and 68°. Therefore, we can set up the following equation:
f + f + 68° = 180°
Solving this gets f = 56°
Bottom Image:
We know that the sum of the angles will add up to 180 and that the angles of the triangle are 23°, 23°, and g. Therefore, we can set up the following equation:
23° + 23° + g = 180°
Solving this gets g = 134°
What are the values of x and y?
Step-by-step explanation:
In figure:
∠PRT+∠RTP+∠TPR=180
O
(angle sum property of triangle)
⇒x+(180
O
−∠RTQ)+60
O
=180
O
(linear pair)
⇒x+(180
O
−97
0
)+60
o
=180
O
⇒x=31
o
Now, ∠PRT+∠TRQ+∠QRS=180
O
(angle of straight line)
⇒x+48
o
+y=180
O
⇒31
o
+48
o
+y=180
O
⇒y=101
0
Find the approximate values of the five-number summary for the data set represented by this box plot.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Answer:
Minimum: 0
Quartile Q1: 22.5
Median: 50
Quartile Q3: 77.5
Maximum: 100
Step-by-step explanation:
Martin has a bag of marbles. He removed 1 marble at random, recorded the color and then placed it back in the bag. He repeated this process several times and recorded his results in a table. Find the experimental probability of drawing green color.
Using it's concept, it is found that there is a 0.3 = 30% experimental probability of drawing green color.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that 15 out of 12 + 10 + 15 + 13 = 50 trials resulted in a green marble, hence the probability is given by:
p = 15/50 = 0.3.
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Points A, B, and Care located on a circle, and chords exist between all three points. If the measure of ZBAC is 88°, what is the measure of BC?
OA. 88°
OB. 92°
O C. 176°
OD. 184°
Answer:
92
Step-by-step explanation:its right
how do you write 10^3 / 10^7 in standard form for properties of exponents
Answer:
1 / 10000
Step-by-step explanation:
10^3 / 10^7
apply exponent rule: x^a / x^b = x^(a-b)
10^3 / 10^7 where a = 3 and b = 7
10^(3 - 7) = 10^(-4)
apply exponent rule: a^-b = 1 / a^b
1 / 10^(4)
10^4 = 10000
1 / 10000
Let me know if you have any questions !
AND WELCOME TO BRAINLY :)
Answer:
10^-4
Step-by-step explanation:
In division of powers (when the numbers are the same), you subtract both the powers. In this case, it would be 3 - 7 = -4, resulting in a power of -4
Solve for D: 70D + 6 - 9D= 35 + 4D - 2.
70d+6-9d=35+4d-2
70d-9d-4d= 35-2-6
57d= 27
d= 27÷57
Which function has zeros of -8, 1, and 3?
Answer:
A?
Step-by-step explanation:
(x-3) (x+8)(x-1) would be the solution
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answer:
The number of walnut pounds we need to add is 10
Step-by-step explanation:
We need to make a mixture that costs $1 per pound.
That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.
[tex]\frac{MixtureCost}{NumberOfPounds} = 1[/tex]
Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.
[tex]MixtureCost = CashewsCost + WalnutsCost[/tex]
We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.
Knowing all of that, we can write this:
[tex]MixtureCost=8*1.25 + x*0.8[/tex]
If we make that multiplication, we have that
[tex]MixtureCost=10+x*0.8[/tex]
Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?
We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:
[tex]NumberOfPounds=8+x[/tex]
Now, if we plug in the values we found in the first equation, here's what we have:
[tex]\frac{10+x*0.8}{8+x}=1[/tex]
The 8+x is dividing, so i'll pass it to the other side multiplying:
[tex]10+0.8*x=x+8[/tex]
The 10 in the left side will go to the right side with a negative sign:
[tex]0.8x=x-2[/tex]
Now, if I pass the x from the right side to the left one changing signs:
[tex]0.8x-x=-2\\\\-0.2x=-2[/tex]
By changing signs from both sides, we have that:
[tex]0.2x = 2\\\\x = 10[/tex]
Therefore, the number of walnut pounds we need to add is 10
Can someone answer theese questions
Question 1 ) A ray has one endpoint and continues forever in the opposite direction
Question 2)
⇒
IG
Question3)
⇒
DC
Hope this helps!
There are 24 students in a class and a decrease of 15%. How many students would you have?
Answer:
20
Step-by-step explanation:
85% of 24 is 20
1/3x + 5 x= -6 need expression 1/3x = 5 is equal to __ when x = -6
Answer:
3
Step-by-step explanation:
To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.
__
1/3(-6) +5 = -2 +5 = 3
For x = -6, the value of the expression is 3.
What is the perimeter of rhombus ABCD?
10 units
20 units
2√7 units
4√7 units
Answer:
The perimeter of the rhombus is 20 units
Step-by-step explanation:
One important fact about a rhombus is that all four of its sides are equal, so we only need to solve for one side in order to find the perimeter. We can use the Pythagorean Theorem to solve the side length of the rhombus. Using line AD as a reference, we know that the length of AD is the square root of the change in x squared plus the change in y squared, or [tex]\sqrt{3^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex] units. Multiply the length of AD by 4 and you'll get that the perimeter of rhombus ABCD is 5 × 4 = 20 un.
The perimeter of the rhombus ABCD is 20 units.
Option B is the correct answer.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add upto 180 degrees.
We have,
We can use the distance formula to find the length of each side of the rhombus, and then add them up to find the perimeter.
The distance between points A and B is:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\= \sqrt{(-2 - 1)^2 + (-3 - 1)^2}\\ = \sqrt{9 + 16}\\= \sqrt(25) \\= 5[/tex]
The distance between points B and C is:
[tex]BC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\= \sqrt{(-5 - (-2))^2 + (1 - (-3))^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\= 5[/tex]
The distance between points C and D is:
[tex]CD = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(-2 - (-5))^2 + (5 - 1)^2}\\ = \sqrt{9 + 16}\\ = \sqrt{25}\\ = 5[/tex]
The distance between points D and A is:
[tex]DA = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(1 - (-2))^2 + (1 - 5)^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\ = 5[/tex]
Since a rhombus has all sides of equal length, we can add up the lengths of the sides to find the perimeter:
P = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20
Therefore,
The perimeter of the rhombus ABCD is 20 units.
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What is the area of this shape?
The area of the composite shape in the image given is calculated as: 316 yd²
How to Find the Area of a Composite Shape?To find the area of a composite shape, find the area of each of the shape that makes up the figure, then add their areas together.
The area of the composite shape = area of big rectangle + area of small rectangle + area of big triangle + area of small triangle
Area of big rectangle = (length)(width) = (5 + 4)(8) = 72 yd²
Area of small rectangle = (length)(width) = (5)(4) = 20 yd²
Area of big triangle = 1/2(base)(height) = 1/2(12)(4+5+4+7) = 120 yd²
Area of small triangle = 1/2(base)(height) = 1/2(8+5)(16) = 104 yd²
The area of the composite shape = 72 + 20 + 120 + 104 = 316 yd²
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I NEED HELP ON THE ONES THAT AREN'T CROSSED OFF!!!!!!!!!!!!!!!!!!!!! PLEASEEEEEEEEEEEEEEEEEEEEE ( i already did 8)
The computation of the word problem shows that the oranges will John have in 12 weeks will be 70 oranges.
How to solve the word problem?The word problem will be that John has 10 oranges and buys 5 more oranges every week. How many oranges will John have in 12 weeks.
The computation will be:
= 10 + 5x
where x= number of weeks.
= 10 + 5x
= 10 + 5(12)
= 10 + 60
= 70 oranges
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HELP PLS
The function of F is defined by f(x)=x+2
find F(n-4)
Answer:
Step-by-step explanation:
f(n - 4)= n - 4 + 2 = n - 2
Find the area of the figure. Round to the nearest hundredth where necessary.
24 m
28 m
what is the answer to this?
The domain of the function is from the point -5 up to infinity that is [-5, infinity)
Domain of a functionThe domain are the independent value of a function for which it exists.
From the given graph, the domain will be the inteval of the function along the x-axis.
From the graph, you can see that the domain of the function is from the point -5 up to infinity that is [-5, infinity)
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On a recent survey, 35% of those surveyed indicated that they preferred running. If 540 people were surveyed, how many people preferred running?
Answer: 189 people preferred running.
Step-by-step explanation: 35% is equal to 35/100. Since 540 people were surveyed, we can multiply 35/100 by 540 to find that 189 people out of 540 preferred running. Hope this helps!
You purchase a hat for $50. There is a sales tax of 8.5%. What is the final cost with sales tax?
Answer:
Price before tax: $ 50.00
+ Sales tax (8.5%): $ 4.25
Total price including tax: $ 54.25
Step-by-step explanation:
A sales tax is a tax that is levied on the purchase of goods and services. Except for Alaska, Delaware, Montana, New Hampshire, and Oregon, all states in the United States and the District of Columbia charge a state sales tax when you buy goods or pay for services. Alaska, like many other states, allows local governments to levy local sales taxes. Certain kinds of goods are exempt from sales tax in some states. In Massachusetts, for example, there is no sales tax on ordinary supermarket goods. There are also extra tax surcharges in several states. Restaurants and motels in the hospitality business sometimes levy a tax rate greater than the state sales tax rate. Expected sales tax rates and potential tax surcharge rates should be checked with your state and area.
Sales Tax Calculation Formulas
Sales tax rate = sales tax percent / 100Sales tax = list price * sales tax rateTotal price including tax = list price + sales tax, orTotal price including tax = list price + (list price * sales tax rate), orTotal price including tax = list price * ( 1 + sales tax rate)What is the surface area?
2 mm
9 mm
3 mm
Answer:
Surface area of rectangular prism
=P×h
=2(l+w)×h
=2(3+9)×2
=48mm²
[tex] \boxed{ \frak{Answer}}[/tex]
Given,
Length (l) = 9 mm
Breadth (b) = 3 mm
Height (h) = 2 mm
To find: The surface of it.
We, know that
Surface area of a cuboid = 2(lb + bh + lh)
By using the formula,
= 2(lb + bh + lh)
= 2(9*3 + 3*2 + 9*2)
= 2( 27 + 6 + 18)
= 2(51)
= 102 mm²
Therefore the required surface area is 102 mm²[tex] \boxed{ \frak{Keep \: Learning }}[/tex]
What is the sum of the first thirteen terms in a geometric series with a
r = 3 a1= -10
The sum of the first thirteen terms of the geometric series is -7971615.
What is Geometric series?This is the sum of an infinite number of terms that has a constant ratio between successive terms.
To calculate the sum of the first thirteen terms of the geometric series, we use the formula below.
Formula:
S₁₃ = a(rⁿ-1)/(r-1).............. Equation 1Where:
S₁₃ = Sum of the first thirteen terms of the geometric series.a = First term of the seriesr = Common ratioGiven:
a = -10r = 3n = 13Substitute these values into equation 1
S₁₃ = -10(3¹³-1)/(3-1)S₁₃ = -7971615Hence, the sum of the first thirteen terms of the geometric series is -7971615.
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