The compound interest formula is:
[tex]A\text{ = P}(1+i)^t[/tex]where:
A is the final amount including the principal
P is the principal amount
i is the interest rate (as a decimal)
t is time in years
Replacing with P = $2650, i = 0.11, and t = 1, we get:
A = 2650*(1 + 0.11)
A = 2650*1.11
A = $2941.5
Hello! I need help with this:Calculation of the confidence interval Statistics.The confidence interval should be calculated for the percentage of people who chose the answer spruce:Sample: 313Answers:Spruce - 272Pine - 41Confidence level - 0.9
We have to calculate a 90% confidence interval for the proportion that chose the answer "Spruce".
The sample proportion is p = 0.869:
[tex]p=\frac{X}{n}=\frac{272}{313}\approx0.869[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_p=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma_p=\sqrt{\frac{0.869\cdot0.131}{313}} \\ \\ \sigma_p\approx\sqrt{0.0003637} \\ \sigma_p\approx0.019 \end{gathered}[/tex]The critical z-value for a 90% confidence interval is z = 1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot\sigma_p=1.645\cdot0.019\approx0.031[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=p-z\sigma_p=0.869-0.031=0.838 \\ UL=p+z\sigma_p=0.869+0.031=0.900 \end{gathered}[/tex]Answer: The 90% confidence interval for the population proportion is (0.838, 0.900).
R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Statement Problem: R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Solution:
R'S'T'U' is a dilation of RSTU by;
[tex]\frac{1}{3}[/tex]because it is reduced by that factor.
CORRECT OPTION: a reduction with scale factor
[tex]\frac{1}{3}[/tex]the table shows the number of incorrect answers given by nine students on a standardized test which of the following measures would make the number of missed questions appear as a small as possible
Let's take them one after the other
To calculate the mean:
Mean = 4 +20+ 5 +10+ 21+ 18 +10+ 11+ 16 / 9
Mean= 115/9= 12.7
To calculate the median;
Median: position (n+1)/2=(9+1)/2=5
This implies it is the fiifth value after ordering them from least to gratest
4, 5, 10, 10, 11, 16, 18, 20, 21
The fifth observation is 11, that's the median
Calculate the range;
Range = highest - lowest = 21 - 4 = 17
Mode = bi modal = 10
The answer is the Mode which is 10
The correct option is the last option : Mode
-12 -24 4bI need help can someone help .
To eliminate the coefficient divide each side by 3
Now solve the two step equation
3g - 5 = 17
3g = 17 + 5 = 22
then g= 22/3
Now solve 9 = 4a + 13
9 -13 = 4a
-4 = 4a then -1= a
a= -1
There are two machines that produce aluminum cans. The newer machine can produce 5700 cans in 190 minutes. It takesthe older machine 285 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5700 cans?
114 minutes
Explanation
Step 1
find the rate of production of each machine (cans per minute)
so
a)The newer machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_1=\frac{5700\text{ cans}}{190\text{ minutes}}=30\text{ }\frac{cans}{minute} \end{gathered}[/tex]b)the older machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_2=\frac{5700\text{ cans}}{285\text{ minutes}}=20\text{ }\frac{cans}{minute} \end{gathered}[/tex]Step 2
Add the rates together to determine their combined
[tex]\begin{gathered} rate_{total}=rate_1+rate_2 \\ rate_{total}=30\text{ }\frac{cans}{minute}+20\frac{cans}{m\imaginaryI nute} \\ rate_{total}=50\text{ }\frac{cans}{minute} \end{gathered}[/tex]so, the total rate( both machine working ) is 50 cans per minute
Step 3
finally, to find the time to produce 5700 cans, divide the total cans by the rate, so
[tex]\begin{gathered} time=\frac{number\text{ of cans}}{rate} \\ time=\frac{5700\text{ cans}}{50\frac{cans}{minute}}=114minutes \\ time=\text{ 114 minutes} \end{gathered}[/tex]therefore, the answer is 114 minutes
I hope this helps you
Which of the following expressions is equivalent to 2^4x − 5? the quantity 8 to the power of x end quantity over 10 the quantity 4 to the power of x end quantity over 5 the quantity 16 to the power of x end quantity over 32 the quantity 1 to the power of x end quantity over 32
The equivalent expression for the given exponent equation is 16^x/32
Given,
The exponent equation; 2^4x - 5
We have to find the expressions which is equivalent to 2^4x - 5
Exponential equations are inverse of logarithmic equations.
This can also be expressed as;
2^(4x-5) = 2^4x/2^5
2^4x-5 =16^x/2^5
2^4x-4 = 16^x/32
Hence the equivalent expression is 16^x/32
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Answer:it's not 4^x/5
Step-by-step explanation:
QUESTION 241 POINTFor a rectangular solid with length 14 feet, height 17 feet, and width 6 feet, find the a. volume and b. surface area.Provide your answer below:volume =cubic feet, surface areasquare feetFEE
The volume and surface area of a rectangular prism are given by the formulas below
[tex]\begin{gathered} V=l*b*h \\ A=2(lb+bh+hl) \\ l\rightarrow\text{ length} \\ w\rightarrow width \\ h\rightarrow\text{ height} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} l=14,w=6,h=17 \\ \Rightarrow V=14*6*17=1428 \\ and \\ A=2(14*6+6*17+17*14)=848 \end{gathered}[/tex]Thus, the answers are: Surface area=848ft^2, and Volume=1428ft^3
The sum of 5 times a number and 7 equals 8. Find the number
Explanation
Let the number be x. Therefore, we will have
[tex]\begin{gathered} 5x+7=8 \\ 5x=8-7 \\ 5x=1 \\ x=\frac{1}{5} \end{gathered}[/tex]determine values of the variables that will make the following equation true, if possible. if not, state “not possible”
Given:
[tex]4\begin{bmatrix}{-r} & & {} \\ {-s} & {} & {} \\ & {} & {}\end{bmatrix}-\begin{bmatrix}{-2r} & & \\ {-2s} & {} & \\ {-2t} & {} & {}\end{bmatrix}=\begin{bmatrix}{-3} & & \\ {-1} & {} & {} \\ {5} & & {}\end{bmatrix}[/tex]As the first matrix has 2 rows and 1 column. And the second matrix has 3 rows and 1 column.
The dimension of both the matrix is not the same.
For the subtraction of two matrices must have the same size.
So, we can not determine the values of variables.
Answer: not possible.
A basket can hold 40 apples. Justin has 22 apples. He plans to buy 7 more. Each apple costs $1.buys the new ones, how many more apples will the basket hold?The basket can hold 15 more apples after Justin buys more.
Answer
Explanation
The basket can hold a maximum of 40 apples.
Justin currently has 22 apples. He plans to buy
Suppose you are in a restaurant and the menu is as follows: 5 beverages, 11 appetizers, 9 main courses, and 3 desserts. Impose the condition that exactly one choice must be made from each category. How many
distinguishable meals can be created?
Answer:
1485
Step-by-step explanation:
The answer is found by multiplying how many of each of the categories there are;
5 × 11 × 9 × 3 = 1485
You are selling drinks at the carnival to raise money for your club. You sell lemonadefor $6 for 2 cups and orange drinks for $9 for 3 cups. Your sales totaled $240. Let xbe the number of cups of lemonade and y be the number of orange drinks. Write anyequation in standard form for the relationship above.
Let x be the number of cups of lemonade sold, and y the number of cups of orange drinks sold, then we can set the following equation:
[tex]6(\frac{x}{2})+9(\frac{y}{3})=240.[/tex]Now, recall that the standard form of a linear equation is:
[tex]Ax+By=C,[/tex]Where, A≥0, B and C are integers.
Simplifying the first equation, we get:
[tex]3x+3y=240.[/tex]Answer:
[tex]3x+3y=240.[/tex]The circle has center O. Its radius is 4 cm, and the central angle a measures 30°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer
Explanation
The area of a portion of a circle with radius 'r' and central angle 'a' in radians is:
[tex]A_{\text{portion}}=\frac{1}{2}\cdot r^2\cdot a[/tex]In this problem, the radius is r = 4cm, and the angle a = 30º.
First we have to express the angle in radians:
[tex]a=30º\cdot\frac{\pi}{180º}=\frac{1}{6}\pi[/tex]And now we can find the area of the shaded region:
[tex]\begin{gathered} A=\frac{1}{2}\cdot(4\operatorname{cm})^2\cdot\frac{1}{6}\pi \\ A=\frac{1}{2}\cdot16\operatorname{cm}^{2}\cdot\frac{1}{6}\pi=\frac{4}{3}\pi \end{gathered}[/tex]Answer
The area of the shaded region is:
[tex]A=\frac{4}{3}\pi cm^{2}[/tex]What are the explicit and recursive formulas for the sequence 540, 180, 60, 20, ...?
Here we have a geometric sequence, the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*540
How to get the recursive formula?
Here we have the following sequence:
540, 180, 60, 20, ...
This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.
180/540 = 1/3
60/180 = 1/3
20/60 = 1/3
So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*A₁
Where A₁ is the first term, in this case 540, so the formula becomes:
Aₙ = (1/3)*ⁿ⁻¹*540
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Rewrite the equation to easily determine the velocity of an object. solve the Equation for v
In order to solve for v in the given equation, follow these steps:
1. Divide both sides of the equation by "m"
[tex]\begin{gathered} E=\frac{1}{2}mv^2 \\ \frac{E}{m}=\frac{1}{2}\frac{mv^2}{m} \\ \frac{E}{m}=\frac{1}{2}\frac{m}{m}v^2 \\ \frac{E}{m}=\frac{1}{2}v^2 \end{gathered}[/tex]2. Multiply both sides by 2
[tex]\begin{gathered} \frac{E}{m}\times2=\frac{1}{2}v^2\times2 \\ 2\frac{E}{m}=\frac{2}{2}v^2 \\ 2\frac{E}{m}=v^2 \end{gathered}[/tex]3. in order to get rid of the exponent of v, take the square root on both sides
[tex]\begin{gathered} \sqrt{2\frac{E}{m}}=\sqrt{v^2} \\ \sqrt[]{2\frac{E}{m}}=v \\ v=\sqrt[]{2\frac{E}{m}} \end{gathered}[/tex]Then, v = √(2E/m)
What is the solution to the following equation?x^2+3x−7=0
Answer:
Explanation:
Given the equation:
[tex]x^2+3x-7=0[/tex]On observation, the equation cannot be factorized, so we make use of the quadratic formula.
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Comparing with the form ax²+bx+c=0: a=1, b=3, c=-7
Substitute these values into the formula.
[tex]x=\dfrac{-3\pm\sqrt[]{3^2-4(1)(-7)}}{2\times1}[/tex]We then simplify and solve for x.
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For each equation in the table, give the slope of the graph.
Answer:
1. undefined
2. 0
3. -6
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept.
Since the equation x = -6 is a vertical line, the slope is undefined.
Since y = -6 is a horizontal line, the slope is 0.
The slope of y = -6x is -6. This is because it is the coefficient of the variable x.
please help need answer asap
Answer:
x = 34 degrees, y = 73
Step-by-step explanation:
Since the triangle is isosceles, the base angles are congruent (equal). First, find the supplement angle by doing 180-107, which gives you 73 for the base angles, which include y. Now there is a theorem that states the 2 remote interior angles are equivalent to the exterior angle, which means 107 = 73 + x. This gives us x = 34
I hope this helps!
Use the same process for the second one.
you bought a car for $5000. each year it depreciates by 8.5%. Which equation can be used to find the value, v, of the car, x years after it was purchased?
We have the following:
In this case, we have the following formula:
[tex]v=C\cdot(1-r)^x[/tex]Where C is the original value of the car, r is the depreciation rate and x is the time in years
How would these look graphed ? Look at image attached .
These are two lines intersected ,in one point
One is positive inclined, the other negative.
Then now GRAPH
THEN BOTH LINES INTERSECT AT
Find the restricted values of x for the following rational expression. If there are no restricted values of x, Indicate "No Restrictions".
−5r – 8/x² + 4
The restricted values of x for the following rational expression.
x = 0
x = -3/4
What are restriction value?Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.
Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.
−5x– 8/x² + 4 = 0
- 5x - 8/[tex]x^{2}[/tex] = -4
x = 0
x = -3/4
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A restaurant has 5 desserts, 3 side dishes and 4 main dishes. A student chooses one side dish, one main dish, and one dessert. How many different meals could he make?
30
Explanation
if the first event occurs in x ways, and the second event occurs in y ways, then two events occur in as sequence of xy ways.
so
event A ; choose (1) dessert , 5 ways
event B , chosen (1) side dish, 3 ways
event C, choose (1) main dish, 2 ways
so
a meal( 1 dessert+1 side dish+main dish) is the product of the 3 ways
[tex]\begin{gathered} \text{ways a meal could be made= (5}\cdot3\cdot2)\text{ ways} \\ \text{ways a meal could be made=}30\text{ ways} \end{gathered}[/tex]therefore, the answer is
30
I hope this helps you
Can you help me resolve this using the quadratic formula?
a) Time taken to hit the ground = 1.674 seconds
b) Height at 1 second = 12 m
Explanation:The equation representing the height of the water balloon after t seconds is:
[tex]h(t)=-16t^2+25t+3[/tex]a) At the ground, h(t) = 0
[tex]\begin{gathered} 0=-16t^2+25t+3 \\ \\ 16t^2-25t-3=0 \\ \\ Using\text{ the quadratic formula} \\ t=\frac{-(-25)\pm\sqrt{(-25)^2-4(16)(-3)}}{2(16)} \\ \\ t=\frac{25\pm\sqrt{817}}{32} \\ \\ t=-0.111975,\text{ 1.67448} \end{gathered}[/tex]Since time cannot be negative:
Time taken to hit the ground = 1.674 seconds
b) Height at t = 1 second
[tex]\begin{gathered} H(t)=-16t^2+25t+3 \\ \\ H(1)=-16(1^2)+25(1)+3 \\ \\ H(1)=-16+25+3 \\ \\ H(1)=12\text{ m} \end{gathered}[/tex]Height at 1 second = 12 m
A translation 6 units right maps P onto P'. Complete the translation function.
If we have a point P=(x,y) and we apply a translation 6 units to the right we will get a point P' that is:
[tex](x,y)\longrightarrow(x+6,y)[/tex]We can test it by trying with P=(0,0).
Then P' would be (6,0), that is 6 units to the right from P.
Answer: (x,y) --> (x+6,y)
5+3x=5x-19 I need help solving Multi Step Equations with Variables on both sides.
The equation we have is:
[tex]5+3x=5x-19[/tex]when we have the variable on both sides of the equation, what we need to do is move all of the variables to one side of the equation.
For example, in this case, to have all of the variables on the same side, we substract 5x to both sides:
[tex]5+3x-5x=5x-19-5x[/tex]On the right side 5x and -5x cancel each other, and we are left with:
[tex]5+3x-5x=-19[/tex]Next, we add the like terms on the left side, 3x-5x is equal to -2x:
[tex]5-2x=-19[/tex]Since we need to solve for x, we substract 5 to both sides, to leave the variable term alone:
[tex]-2x=-19-5[/tex][tex]-2x=-24[/tex]And finally, we divide both sides by -2:
[tex]\begin{gathered} -\frac{2x}{-2}=\frac{-24}{-2} \\ \\ x=12 \end{gathered}[/tex]Answer: x=12
Solve the problems. Simon is organizing his 36 toy cars into equal-sized piles. Which list shows all of the possible numbers of cars that could be in each pile? A 2. 3,4,6 B 1, 2, 3, 4,6 C 2, 3, 4, 6, 9, 12, 18 D 1, 2, 3, 4, 6, 9, 12, 18, 36
Consider that the total available toy cars is 36.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
So Simon can make 1 pile of 36 toy cars, 2 piles of 18 cars each, 3 piles of 12 cars each, 4 piles of 9 cars each, 6 piles of 6 cars each, 9 piles of 4 cars each, 12 piles of 3 cars each, 18 piles of 2 cars each, and 36 piles of 1 car each.
Thus, the possible number of cars that could be in each pile are 1,2, 3, 4, 6, 9, 12, 18, 36.
Therefore, option D is the correct choice.
What is the missing number 100 -11- missing number -12=9
Answer:
68
Step-by-step explanation:
100-68-12-11=9
12+11=23
100-23-9=68
I need help on a problem
As shown in the figure:
AB || CD
AD || CB
We need to prove AB = CD
So, the proof will be as follows:
Statements Reasons
0. AB || CD Given
,1. m∠BAC = m∠DCA Alternate angles are congruent
,2. AD || CB Given
,3. m∠BCA = m∠DAC Alternate angles are congruent
,4. AC = CA Reflexive property
,5. ΔBAC ≅ ΔDCA By A.S.A [angle-side-angle] postulate
,6. AB ≅ CD CPCTC
Mark the drawing to show the given information and complete each congruence statement.∆acd=∆_____by______
the triangle is ACD is equal to the triangle CBE so let write all the information we have in the figure so:
And for oposit angles we know that then angle BCE = to the angle ACD, so we have two angles and ine side equal so the triangles are similar
by: ASA
the running trail in the local park is 3.826 miles long. If the park board were planning to extend the trail by 2.46 miles, what would the new length of the running trail be?
The running trail is 3.826 miles long. If we add 2.46 miles, the new length will be:
[tex]3.826miles+2.46\text{ miles}[/tex]which gives 6.286 miles. Then, the new lenght will be 6.286 miles long.
