If scores on a standardized reading test form a normal distribution with (µ = 60) and (σ = 20), then the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16) will be .
As per the question statement, Scores on a standardized reading test for fourth-grade students form a normal distribution with (µ = 60) and (σ = 20),
And we are required to calculate the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16).
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 60), standard deviation (σ = 20) and a sample size of (n = 16).
Then the probability that a sample of size (n = 16) is randomly selected with a mean greater than 65 can be calculated as follows:
P(M > 65) = [1 - P(M < 65)]
= [1 - P{(M - μ)/(σ/√n) < (65 - 60/(20/√16)}]
= [1 - P{(M - μ)/(σ/√n) < (65-60)/(20/4)}]
= [1 - P{Z < (5/5)}]
= [1 - P(Z < 1)]
= (1 - 0.841344746069)...[Using Excel Function "NORMSDIST (1)]
= 0.158655253931
≈ 0.16
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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what would be the cost of 707 square feet of topsoil at the price of $1.25 per square foot
Answer:
$883.75
Explanation:
The cost of 1 square foot of topsoil = $1.25.
Thus, the cost of 707 square feet of topsoil:
[tex]\begin{gathered} =707\times\$1.25 \\ =\$883.75 \end{gathered}[/tex]Find the distance from the point to the line Y=-1x-3 and Q (2,3)
Solution
We can do the following:
Ax + By + C= 0
Rewriting the line we got:
1x +1y +3=0
And the point is: (x= 2, y= 3)
and we can use the following formula:
[tex]d=\frac{|Ax_1+By_1+C|}{\sqrt[]{A^2+B^2}}=\frac{|1\cdot2+1\cdot3+3|}{\sqrt[]{1^2+1^2}}=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=4\sqrt[]{2}[/tex]
At Hayley’s Beading Boutique there are 23 plastic beads and 2 metal beads on clearance. What percentage of the beads on clearance are plastic? PLEASE ANSWER!!!
The percentage of the beads on clearance are plastic is 92%.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that At Hayley’s Beading Boutique there are 23 plastic beads and 2 metal beads on clearance.
The percentage will be calculated as,
P = 23 / 25
P = 0.92
Multiply by 100 to convert into a percentage,
P = 92%
Therefore, the percentage of the beads on clearance are plastic is 92%.
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i need help with this problem..Yolanda took out a 30-year mortgage for $80,000 at 10% How much wills he pay over money year? i assume 2666.66
Step 1:
Most mortgages are also simple interest loans, although they can certainly feel like compound interest. In fact, all mortgages are simple interest except those that allow negative amortization. An important thing to pay attention to is how the interest accrues on the mortgage.
Step 2:
[tex]Interest\text{ = }\frac{Prt}{100}\text{ }[/tex]Step 3:
Write the given data
P = $80000
t = 30 years
r = 10%
Step 4
[tex]\begin{gathered} \text{Interest = }\frac{80000\text{ }\times\text{ 30 }\times\text{ 10}}{100} \\ \text{Interest = \$240000} \end{gathered}[/tex]Final answer
Interest = $240000
How do you use the following formulas for an equation like this?
Let's begin by listing out the information given to us:
|CD| = 9.5, |CE| = 13.75, |AC| = 13.75 + 5.5 = 19.25, |BC| = 9.5 + x
Using Triangle proportionality theorem, we have:
[tex]\begin{gathered} |CE|\colon|EA|=|CD|\colon|DB| \\ 13.75\colon5.5=9.5\colon x\Rightarrow\frac{13.75}{5.5}=\frac{9.5}{x} \\ 13.75x=5.5\cdot9.5 \\ \frac{13.75x}{13.75}=\frac{5.5\cdot9.5}{13.75}\Rightarrow x=\frac{5.5\cdot9.5}{13.75} \\ x=3.8 \\ \\ \therefore|BD|=3.8 \end{gathered}[/tex]Write –9 43/100 as a decimal number
Let's rewrite the mixed number as a fraction, using the following formula:
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}_{}[/tex]So:
[tex]-(9\frac{43}{100})=-(\frac{9\cdot100+43}{100})=-(\frac{900+43}{100})=-\frac{943}{100}[/tex]To write -943/100 we can use long division, or since we are dividing by 100 we can simply move the decimal point two units to the left, so:
[tex]-\frac{943}{100}=-9.43[/tex]Answer:
-9.43
Find the length of a diagonal ofa square with sides of 10inches long.[?]V ] inches
the Given:
The side of the square is a = 10 inches.
Explanation:
The length of the diagonal of the square is determined by Pythagoras theorem.
[tex]\begin{gathered} d=\sqrt[]{a^2+a^2} \\ =\sqrt[]{2a^2} \\ =\sqrt[]{2}a \end{gathered}[/tex]Substitute 10 for a in the equation to determine the length of the diagonal of the square.
[tex]\begin{gathered} d=\sqrt[]{2}\cdot10 \\ =10\sqrt[]{2} \end{gathered}[/tex]So the answer is,
[tex]10\sqrt[]{2}[/tex]The container that holds the water for the football team isfull. After pouring out 5 gallons of w2gallonsХ5?
Answer:
25 gallons
Explanation:
Let's call x the number of gallons that the container can hold.
The container starts half full, so it starts with (1/2)x gallons, then they pour out 5 gallons to let the container 3/10 full, so we need to subtract 5 gallons to get (3/10)x gallons. It means that we can write the following equation
[tex]\frac{1}{2}x-5=\frac{3}{10}x[/tex]Now, we can solve the expression for x, so
[tex]\begin{gathered} \frac{1}{2}x-5+5=\frac{3}{10}x+5 \\ \frac{1}{2}x=\frac{3}{10}x+5 \\ \frac{1}{2}x-\frac{3}{10}x=\frac{3}{10}x+5-\frac{3}{10}x \\ \frac{1}{5}x=5 \\ 5\cdot\frac{1}{5}x=5\cdot5 \\ x=25 \end{gathered}[/tex]Therefore, the container can hold 25 gallons.
Rick shoots a basketball at an angle of 60' from the horizontal. It leaves his hands 6 feet from the ground with a velocity of 25 ft/s.Step 1 of 2: Construct a set of parametric equations describing the shot. Answer
Solution:
Given:
[tex]\begin{gathered} Initial\text{ velocity,}u=25ft\text{ /s} \\ \theta=60^0 \end{gathered}[/tex]
The parametric equations are gotten by first resolving the velocity into horizontal and vertical components.
Recall;
[tex]\begin{gathered} speed=\frac{distance}{time} \\ distance=speed\times time \end{gathered}[/tex]Hence, the parametric equations are:
[tex]\begin{gathered} x=(25cos60)t \\ y=(25sin60)t+6 \end{gathered}[/tex]which number is in the tenths place : 123.456?Round the following number to the tenths place: 123.456?
Answer:
The number in the tenths place is
[tex]4[/tex]Rounding the number to the tenths place, we have;
[tex]123.5[/tex]Explanation:
Given the number;
[tex]123.456[/tex]The number in the tenths place is the first number after the decimal point. Which is;
[tex]4[/tex]Rounding the number to the tenths place, we have;
[tex]123.456\approx123.5\text{ (to the nearest tenth)}[/tex]If m = 2 and n = 3 then, evaluate 1*m*3 + 2*n*2 + 4
Given:
[tex]1\times m\times3+2\times n\times2+4[/tex]Substitute the value of m=2 and n=3 into the
An accountant executive had car expenses of $1025.58 for insurance, $1805.82 for gas, $37.92 for oil, and $288.27 for maintenance during the year in which 11,320 miles were driven. Find the cost per mile for these four items taken as a group. Round to the nearest tenth of a cent.
Answer:
The cost per mile for each and all the expenses is;
[tex]\begin{gathered} \text{For insurance: = 9.1 cents/mile} \\ \text{For gas: = 16.0 cents/mile} \\ \text{ For oil: = 0.3 cents/mile} \\ \text{ For maintenance: = 2.5 cents/mile} \\ \text{ Total cost per mile: = 27.9 cents/mile} \end{gathered}[/tex]Explanation:
Given that;
An accountant executive had car expenses of $1025.58 for insurance, $1805.82 for gas, $37.92 for oil, and $288.27 for maintenance during the year.
The sum of the four expenses is;
[tex]\begin{gathered} T=\text{ \$1025.58 + \$1805.82 + \$37.92 + \$288.27} \\ T=\text{ \$3157.59} \end{gathered}[/tex]During the year it travels 11,320 miles.
The cost per mile for each of the items are;
For Insurance;
[tex]\begin{gathered} \frac{\text{ \$}1025.58}{11320} \\ =\text{ \$0.09 per mile} \\ =9.1\text{ cents/mile} \end{gathered}[/tex]For gas;
[tex]\begin{gathered} \frac{\text{ \$1805.82}}{11320} \\ =\text{ \$0.1595 per mile} \\ =16.0\text{ cent/mile} \end{gathered}[/tex]For oil;
[tex]\begin{gathered} \frac{\text{ \$37.92}}{11320} \\ =0.0033 \\ =0.3\text{ cents/mile} \end{gathered}[/tex]For maintenance;
[tex]\begin{gathered} \frac{\text{ \$288.27}}{11320} \\ =0.0254 \\ =2.5\text{ cents/mile} \end{gathered}[/tex]The total cost per mile will be;
[tex]\begin{gathered} \frac{\text{ \$3157.59}}{11320} \\ =0.2789 \\ =27.9\text{ cents/mile} \end{gathered}[/tex]The cost per mile for each and all the expenses is;
[tex]\begin{gathered} \text{For insurance: = 9.1 cents/mile} \\ \text{For gas: = 16.0 cents/mile} \\ \text{ For oil: = 0.3 cents/mile} \\ \text{ For maintenance: = 2.5 cents/mile} \\ \text{ Total cost per mile: = 27.9 cents/mile} \end{gathered}[/tex]Rewrite cot 24° in terms of its cofunction.cot 24° =(Type an exact answer. Simplify your answer. Type any angle measures in degrees.
Given the angle = 24
the complementary angles have a sum of 90
The complemantry angle of 24 will be = 90 - 24 = 66
so, cot 24 = tan 66
So, the answer will be tan 66
f(x) = 3x^2 + 6x - 59(x) = 4x^3 - 5x^2+ 6Find ( f + g)(x).
3x² + 6x - 5 = f(x)
+
4x³ - 5x² + 6 = g(x)
----------------------------
4x³ - 2x² + 6x + 1 = (f+g)(x)
Consider the two triangles, which are not drawn to scaleFor the two triangles to be similar by angle-angle similarity, which values could be x be?A. 27 or 115B. 38 or 77C. 52 or 77D. 115 or 153
Recall that the Angle-Angle criterion states that two triangles are similar if two of their angles are congruent.
Now, recall that the interior angles of a triangle add up to 180 degrees, therefore, the other side of the largest triangle has measure
[tex]180^{\circ}-115^{\circ}-38^{\circ}=27^{\circ}.[/tex]Therefore, the values that x could be are:
[tex]27\text{ or 115.}[/tex]Answer: First option.
[tex]27\text{ or 115.}[/tex]the price of a calculator with discount of 45% which fraction is equal to 45%
Explanation
The price of the calculator is discounted 45%al
A musician plans to perform 5 selections. In how many ways can the musician arrange the musical selections?
Given:
A musician plans to perform 5 selections.
To find the total number of possible ways he can arrange the musical selections:
At the first time, there are 5 possibilities to make the musical selections.
At the second time, there will be 4 possibilities to make the musical selections.
At the third time, there will be 3 possibilities to make the musical selections.
At the fourth time, there will be 2 possibilities to make the musical selections.
At the fifth time, there will be 1 possibility to make the musical selections.
So, we have,
[tex]\begin{gathered} ^5C_1\times^4C_1\times^3C_1\times^2C_1\times^1C_1=5\times4\times3\times2\times1 \\ =120\text{ ways} \end{gathered}[/tex]Hence, the answer is 120 ways.
find the difference. you nay use a number line to help you find your answer7 - (-0.9) =
7-(-0.9)
7+ 0.9 = 7.9
Number line:
If A={g,y,m,n,a,s,t,i,c} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′.
Step 1:
What is the complement of set A' ? are elements or members of set A that are not in the universal set U.
Step 2
Set A = {g,y,m,n,a,s,t,i,c}
Universal set U = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}
Step 3:
A' = {b, d, e, f, h, j, k, l, o, p, q, r, u, v, w, x, z}
Final answer
A' = {b, d, e, f, h, j, k, l, o, p, q, r, u, v, w, x, z}
The table shows the amounts of onions and tomatoes in batches of different sizes in a sauce recipe.Elena observes that if she takes the number in the column for tomatoes and divides it by the corresponding number in the column for onions, she always gets the same result.What is the meaning of the number that Elena calculated?onions (ounces)246tomatoes (ounces)163248More about this source textSource text required for additional translation informationSend feedbackSide panels
The number that Elena calculated is the constant of proportionality, which express the ratio of two proportional quantities. In this case, it expresses how much does the amount of tomatoes vary when the amount of onions varies, this is a directly proportional relationship.
using the points that are given, what is the slop of this line?
I tried everything I could to answer this question but I couldn’t get it
We need to use some properties of the kyte:
· The opposite obtuse angles are equal. In the figure, this means ∠WZY = ∠WXY
· The large diagonal bisects the angles ∠ZWX and ∠XYZ
56 ask us to find m∠XYZ. We can note that the angles ∠ZXY and ∠XZY are congruent. And we know that the interior angles of the triangle XYZ add to 180º.
m∠VXY = m∠VZY = 58º
Then:
[tex]\begin{gathered} m∠ZXY+m∠XZY+m∠XYZ=180º \\ 58º+58º+m∠XYZ=180º \\ m∠XYZ=64º \end{gathered}[/tex]The answer to 56. is 64º
57 ask us to find m∠ZWV, we can use the second property listed above. The large diagonal bisects the angle ∠ZWX. Since we know ∠ZWX = 50º, then:
[tex]\begin{gathered} m∠ZWV=\frac{1}{2}\cdot m∠ZWX \\ . \\ m∠ZWV=\frac{1}{2}\cdot50º=25º \end{gathered}[/tex]The answer to 57 is 25º
58 ask us to find m∠VZW. We know that the sum of all internal angles of a kite (or any quadrilateral), is 360º.
We know:
m∠ZWX = 50º
m∠WZY = m∠WXY
m∠XYZ = 64º
Then:
[tex]\begin{gathered} m∠ZWX+m∠WZY+m∠WXY+m∠XYZ=360º \\ 50º+2m∠WZY+64º=360º \\ 2m∠WZY=360º-114º \\ m∠WZY=\frac{1}{2}\cdot246º \\ m∠WZY=123º \end{gathered}[/tex]And:
[tex]m∠WZY=m∠VZW+m∠VZY[/tex]Now replace the known values of m∠WZY = 123º and m∠VZY = 58º:
[tex]\begin{gathered} 123º=m∠VZW+58º \\ m∠VZW=123º-58º=65º \end{gathered}[/tex]The answer to 58 is 65º
59 ask us to find m∠WZY, we sis it in 58 to find m∠VZW.
The answer to 59 is 123º
Two angles are supplementary angles if the sum of their measures is 180. Find the measures of two supplementary angles if the measure of one angle is 4 degrees less than three times the other.What are the measures of the two angles?
Answer:
The measures of the two angles are 46° and 134°.
Explanation:
Let x and y be the two angles:
x+y=180
It is mentioned that the measure of one angle is 4 degrees less than three times the other.
Let:
y=3x-4
Then, we substitute y=3x-4 into x+y=180.
So,
[tex]\begin{gathered} x+y=180 \\ x+(3x-4)=180 \\ \text{Simplify and rearrange} \\ x+3x-4=180 \\ 4x=180+4 \\ 4x=184 \\ x=\frac{184}{4} \\ \text{Calculate} \\ x=46 \end{gathered}[/tex]We substitute x=46 into x+y=180. So,
[tex]\begin{gathered} x+y=180 \\ 46+y=180 \\ \text{Simplify and rearrange} \\ y=180-46 \\ \text{Calculate} \\ y=134 \end{gathered}[/tex]Therefore, the measures of the two angles are 46° and 134°.
Since f is parallel to line g, use the diagram to the right right to answer the following question (I need help with problem D and the graph right next to it )
Given,
The line f and g are parallel lines.
a)The measure of angle 2 is 117 degree.
By exterior atlernate angle property,
[tex]\begin{gathered} \angle2=\angle7 \\ \angle7=117^{\circ} \end{gathered}[/tex]The measure of angle 7 is 117 degree.
b)The measure of angle 4 is 68 degree.
By sum of adjacent angle between two parallel lines property,
[tex]\begin{gathered} \angle4+\angle6=180^{\circ} \\ \angle6=180^{\circ}-68^{\circ} \\ \angle6=112^{\circ} \end{gathered}[/tex]The measure of angle 6 is 112 degree.
c)The measure of angle 5 is 32 degree.
By alternate interior angle property,
[tex]\begin{gathered} \angle4=\angle5^{} \\ \angle4=32^{\circ} \end{gathered}[/tex]The measure of angle 4 is 32 degree.
d)The measure of angle 7 is 121 degree.
By corresponding angle property,
[tex]\begin{gathered} \angle7=\angle3^{} \\ \angle3=121^{\circ} \end{gathered}[/tex]The measure of angle 3 is 121 degree.
Hint: You should have three pairs of congruent corresponding angles AND three pairs of congruent corresponding sides.
The corresponding pairs of the two congruent triangles △AEC ≅ △BFD are:
∠A ≅ ∠B∠E ≅ ∠F∠C ≅ ∠DAE ≅ BFEC ≅ FDAC ≅ BDWhat is the congruency of triangles?Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. You can move, flip, twist, and turn these triangles to produce the same effect.So, the corresponding pairs of the given congruent triangles will be:
We know that all angles and sides are equal.Then, we have:
∠A ≅ ∠B∠E ≅ ∠F∠C ≅ ∠DAE ≅ BFEC ≅ FDAC ≅ BDTherefore, the corresponding pairs of the two congruent triangles △AEC ≅ △BFD are:
∠A ≅ ∠B∠E ≅ ∠F∠C ≅ ∠DAE ≅ BFEC ≅ FDAC ≅ BDKnow more about the congruency of triangles here:
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What is the probability of rolling a die one time and having it land on a number greater than 4?
Let:
n = Number of outcomes = 6
A = roll a number greater than 4 = 2
Therefore:
[tex]\begin{gathered} P(A)=\frac{A}{n} \\ P(A)=\frac{2}{6}=\frac{1}{3}=0.33 \end{gathered}[/tex]Answer:
33%
6) 1,4,9,_,25,_,_,_,81Explain and fill the sequence, write the explicit and recursive formula for the sequence
Answer:
Explanation:
Here, we want to fill the sequence, write the recursive and explicit formulae
From the sequence, we can see that each of the numbers are perfect squares
Depending on the term, the number is squared
Take for example, 1^2 is 1, 2^2 is 4
The correct way of filling is thus to raise the term number to 2
So, we have to fill for the 4th term, the 6th term, the 7th term and the 8th term
We have that as follows:
[tex]\begin{gathered} 4thterm=4^2\text{ = 16} \\ 6thterm=6^2\text{ = 36} \\ 7thterm=7^2\text{ = 49} \\ 8thterm=8^2\text{ = 64} \end{gathered}[/tex]The sequence can then be written as:
[tex]1,4,9,16,25,36,49,64,81[/tex]Now, we want to write the explicit and recursive formula
The explicit formula is written in a way that it does not consider the term before the present term
We can easily write that as:
[tex]T_n=n^2[/tex]For the recursive formula, we write it as a mathematical function that takes into account the term before or after the current term
A point to note that there are odd number differences that increase by 3 as we move from term to term
We can see that:
Term 2 minus Term 1 is 3
Term 3 minus Term 2 is 5
Term 4 minus Term 3 is 7
Term 5 minuus Term 4 is 9
Thus, we have the recursive formula as:
[tex]\begin{gathered} T_n=T_{(n-1)}\text{ + n + n-1} \\ T_n=T_{(n-1)\text{ }}+\text{ 2n-1} \end{gathered}[/tex]I need to know 3 equivalent expressions for the total amount of money.
we can rewrite the expression with a factor
[tex]M=5(8pd+5pd+20d)[/tex]and we can rewrite again with the other factor "d"
[tex]\begin{gathered} M=5d(8p+5p+20) \\ M=5d(13p+20) \end{gathered}[/tex]A = bh; solve for h
Given the equation:
[tex]A=b\cdot h[/tex]It's required to solve it for h, that is, isolate h as the only letter on the left side of the equation.
First, swap sides.
[tex]b\cdot h=A[/tex]Then, divide both sides of the equation by b:
[tex]\frac{b\cdot h}{b}=\frac{A}{b}[/tex]Simplify the left side:
[tex]h=\frac{A}{b}[/tex]Jill mixes two types of concentrations of HCI (hydrochloric acid): 0.375 liters of 25% hydrochloric acid, and 0.625 liters of 65% hydrochloric acid. What is the HCI concentration of the mixed solution? O 56% O 40% O 50% O 446
Given:
Jill mixes two types of concentrations of HCI (hydrochloric acid):
a.) 0.375 liters of 25% hydrochloric acid and 0.625 liters of 65% hydrochloric acid.
To be able to find the final HCL concentration, we will be generating the following formula:
[tex]\text{ Original + Added = Result}[/tex][tex](0.375)(\frac{25}{100})\text{ + (0.625)(}\frac{65}{100})\text{ = (x)}(0.375\text{ + 0.625)}[/tex]Where,
x = the final concentration of HCL
Let's find x,
[tex](0.375)(\frac{25}{100})\text{ + (0.625)(}\frac{65}{100})\text{ = (x)}(0.375\text{ + 0.625)}[/tex][tex](0.375)(0.25)\text{ + (0.625)(0.65) = (x)(}1)[/tex][tex]0.09375\text{ + 0.40625 = x}[/tex][tex]0.5\text{ = x }\rightarrow\text{ x = 0.5}[/tex][tex]\text{ x = 0.5 x 100 = 50\%}[/tex]Therefore, the final concentration of the mixed solution is 50%.