Given:
The diameter of a circle is 20 inches.
So, d = 20 inches
We will find the radius of the circle (r)
The diameter is two times the radius
Or, we can say, the radius is half of the diameter
so, r = d/2 = 20/2 = 10 inches
so, the answer will be The radius = 10 inches
Suppose that $21,800 is invested in a certificate of deposit for 3 years at 9.6% annual interest to be compounded semi-annually. How much interest will this investment earn? Round your answer to the nearest cent, if necessary.
The total compound interest is $7,081.8 , which interest will this investment earn.
What is compound interest?
Compound interest is interest that builds up over a set length of time on both principal and interest. The principal is also used to account for the interest that has accrued on a principal over time.Interest on the principal plus compounded interest is known as compound interest.Initial balance= 21,800$
Interest rate =9.6%
Term=3yrs0mos
Compounding frequency=semi-annually (2/Yr)
CI= P(1+(r/n)^nt-P
The final balance is $28,881.8.
The total compound interest is $7,081.8.
The total compound interest is $7,081.8 , which interest will this investment earn.
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Solve the system of equations using a table and graph. X-2y=3. Y+3x=-5
[tex]x = 3 + 2y.....(3)equation[/tex]
[tex]y + 3(3 + 2y) = - 5 \\ y + 9 + 6y = - 5 \\ y + 6y = - 5 - 9 \\ 7y = - 14 \\ \frac{7y}{7} = \frac{ - 14}{7} \\ y = - 2[/tex]
[tex]x = 3 + 2y \\ x = 3 + 2( - 2) \\ x = 3 - 4 \\ x = - 1[/tex]
ATTACHED IS THE SOLUTION.
Write a coordinate proof: Given: Coordinates of triangle DEF, H is the midpoint of DA, G is the midpoint of EA . Prove: Side DG is congruent to side EH Here is the image down below. I have to fill in the blanks with each of the correct choices that are provided down below.
SOLUTION
Consider the image in the below
From the diagram above,
[tex]\begin{gathered} H\text{ is the mid point of AD} \\ \text{And } \\ G\text{ is the midpoint of AE} \end{gathered}[/tex]Then we obtain the coordinate of H and G
Using the coordinate of midpoint formula,
[tex]\begin{gathered} \text{Coordinate of H is } \\ (-\frac{2h+0}{2},\frac{2k+0}{2})=(\frac{-2h}{2},\frac{2k}{2})=(-h,k) \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{Coordinate of G } \\ (\frac{2h+0}{2},\frac{2k+0}{2})=(\frac{2h}{2},\frac{2k}{2})=(h,k) \end{gathered}[/tex]Then use the distance formula to fined the lenght of |EH| and |DG|
The Distance formula is given by
[tex]\text{Distance}=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Hence
[tex]\begin{gathered} U\sin g\text{ the coordinatesH= (-h,k) and E= (2h,0) } \\ \text{Then} \\ |EH|=\sqrt[]{(2h-(-h)^2+(0-k)^2} \\ |EH|=\sqrt[]{(3h)^2+(-k)^2} \\ \text{Then } \\ |EH|=\sqrt[]{9h^2+k^2} \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{ Using the coordinatesG= (h,k) and D=(-2h,0) for |DG|} \\ |DG|\text{ =}\sqrt[]{(-2h-h)^2+(0-k)^2} \\ |DG|=\sqrt[]{(-3h)^2^{}+(-k)^2} \\ \text{hence } \\ |DG|-=\sqrt[]{9h^2+k^2} \end{gathered}[/tex]
Hence
Since we obtain the same expression above
Then
[tex]\begin{gathered} |EH|=|DG| \\ or \\ |DG|=|EH| \end{gathered}[/tex]therefore
[tex]|DG|\cong|EH|[/tex]Therefore
Answer: DG is congruent to side EH
Which property is shown here?10 + (4 + 7b) = (10 + 4) + 7bDistributive PropertyAssociative Property of AdditionAssociative Property of MultiplicationCommutative Property of AdditionCommutative Property of Multiplication> Next Question
the property shown is the Cummulative Property of Addition
10 + (4 + 7b) = 14 + 7b
(10 +
Francisco is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 74, find Francisco's age.
Answer:
Francisco is 17.
Step-by-step explanation:
Francisco is the youngest. This means that his three siblings are all older than he is.
Let
x = Francisco's age
"Consecutive" means that the ages of the siblings are in a row, like stairsteps. He is the youngest and the others are +1, +1 , +1.
The ages are x and x+1, the next one x+2 and the oldest is x+3.
x+x+1+ x+2 + x+3=74
The question said the sum of their ages is 74. "Sum" means we add the ages.
x+x+1+x+2+x+3 = 74
Combine like terms.
4x + 6 = 74
Subtract 6.
4x + 68
Divide by 4.
x = 17
Francisco is 17.
Check:
Francisco is 17, so his brothers or sisters are 18, 19, and 20.
17 + 18+19+20 = 74
74 = 74 Check!
A line passes though two points A(-2, 2). B(-1, 2). What is the slope:
Answer:
The slope is 0
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Where the values of x and y are from the known points
Here the points are (-2,2) and (-1,2)
So we have (x1,y1) = (-2,2) and (x2,y2) = (-1,2)
This means, x1 = -2 , x2 = -1 , y1 = 2 and y2 = 2
We now plug these values into the slope formula
Recall slope = (y2 - y1) / (x2 - x1)
==> plug in x1 = -2 , x2 = -2 , y1 = 2, y2 = 2
Slope = (2 - 2) / (-1 - (-2)
==> remove parenthesis
Slope = (2-2) / (-1 + 2)
==> simplify addition and subtraction
Slope = 0 / 1 = 0
if 32 is added to the data set which statement is true
We have a dataset: 13, 6, 13, 8, 2, 19, 11, 16, 17, with size n = 9.
We will add 32 to it.
In this case, the mean will be affected, as it depends on each individual value of the dataset. As the number is greater than all the numbers in the dataset, it will be greater than the actual mean. Then, the mean will increase.
The median may or may not change, depending on the values of the set.
Then, we can find the median before and after the addition.
First, we have to sort the data: 2, 6, 8, 11, 13, 13, 16, 17, 19.
The median, for a size n =9, will be located in the fifth place, so the median is 13.
Then, the dataset has 4 values below and 4 values above the median.
When we add 32, it will be the greatest value, so we will have a dataset of size n =10 and sorted as: 2, 6, 8, 11, 13, 13, 16, 17, 19, 32.
The median will be the average between the fifth and sixth place. Both values are 13, so the average, and therefore, the median will be also 13.
Then, in this case, the mean increases but the median does not.
Answer: The mean will increase and the median will remain the same.
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 8. Find the numbers.
Answer:
Let your two numbers be n and n-1. Then: 2n+n²-2n+1=51 n²=50 n=5√2 n-1=5√2-1
Hope that helps <3
Linus what to buy ribbon to make three bookmarks. One bookmark will be 14,5 inches long and the other two will be 9,25 inches long. How much ribbon should he buy in centimeters ( assume 1 inche=0,0254 meters)
Given:
ribbon's long as 14.5 inches one and 9.25 inches two ribbons.
Total ribbon needed = 14.5+2(9.25)
[tex]\text{Total ribbon needed}=14.5+18.5[/tex][tex]\text{Total ribbon needed}=33\text{ inches}[/tex][tex]\text{Total ribbon needed}=33\times0.0254\times100\text{ cm}[/tex][tex]\text{Total ribbon needed}=83.82\text{ cm}[/tex]Therefore, He should but 83.82 cm long ribbon.
find the missing value of the probability distribution
I inserted the link to the question. please help asap
The missing value of the probability distribution is 0.05.
What is the probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
X : 0 1 2 3 4
P(X) : 0.30 0.25 0.25 0.15 ?
A discrete probability distribution function has two characteristics:
Each probability is between zero and one, inclusive. The sum of the probabilities is one.P(X = 4) = 1 - (0.30 + 0.25 + 0.25 + 0.15)
Apply the addition operation,
P(X = 4) = 1 - 0.95
Apply the subtraction operation to get
P(X = 4) = 0.05
Therefore, the missing value of the probability distribution is 0.05.
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Hi, can you help me answer this question please, thank you
We have the following information from the question:
[tex]\begin{gathered} sample\text{ size, n=18} \\ \text{standard deviation=0.4} \\ \text{sample mean, }\bar{\text{x}}=\frac{sum\text{ of data values}}{\text{number of data values}} \\ \bar{x}=\frac{3149.94}{18} \\ \bar{x}\cong175 \end{gathered}[/tex]a) To get the critical value, we would find the significance level first.
Thus, we have:
[tex]\begin{gathered} \text{Significance level, }\alpha=1-confidence\text{ interval} \\ C.I=80\text{\%=0.8} \\ \alpha=1-0.8 \\ \alpha=0.2 \end{gathered}[/tex][tex]\begin{gathered} \text{Critical value=Z}_{\frac{\alpha}{2}}=Z_{\frac{0.2}{2}}=Z_{0.1}=1.28\text{ ( from the z-table)} \\ \text{Therefore, critical value=}\pm\text{1.28}0 \end{gathered}[/tex][tex]\begin{gathered} S\tan dard\text{ deviation of the sample mean, }\sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}} \\ \sigma_{\bar{x}}=\frac{0.4}{\sqrt[]{18}}=0.0943 \end{gathered}[/tex]b) To find the confidence interval, we have to obtain the Margin of Error first.
[tex]\text{Margin of Error,E}=\text{critical value}\times\text{standard deviation of the sample mean(standard error)}[/tex][tex]\begin{gathered} E=1.28\times0.0943 \\ E=0.1207 \end{gathered}[/tex]Therefore, the Confidence Interval is:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex][tex]\begin{gathered} 175-0.1207<\mu<175+0.1207 \\ 174.88<\mu<175.12 \end{gathered}[/tex]Each of the 6 students reported the number of movies the saw in the past year.11, 17, 11,8, 15, 9find the Median & Mean number of movies that each student saw round to the nearest tenth
Solution
The median is the middle number in a sorted, ascending or descending, list of numbers
We need to arrange them in ascending order
8, 9, 11, 11, 15, 17
The middle numbers are 11 and 11
Median = (11 + 11)/2 = 11.
Mean is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list.
[tex]\text{ Mean}=\frac{8+9+11+11+15+17}{6}\approx11.8[/tex]Median is 11
The mean is 11.8
Type the correct answer in the box. The area is ___ (BLANK) square units.
The figure is a trapezoid, and the area of a trapezoid can be calculated with the formula below:
[tex]A=\frac{(B+b)h}{2}[/tex]Where B is the greater base, b is the smaller base and h is the height.
To find the measure of the smaller base, we need to find the missing piece to the right of the value "3 units" (let's call it x).
To calculate it, we can use the total length of the greater base:
[tex]\begin{gathered} 9+x+3=21\\ \\ 12+x=21\\ \\ x=21-12\\ \\ x=9 \end{gathered}[/tex]Therefore the smaller base is 3 + 9 = 12 units.
Now, calculating the trapezoid area, we have:
[tex]A=\frac{(21+12)5}{2}=\frac{33\cdot5}{2}=82.5\text{ u^^b2}[/tex]What is the surface area of this design? 5 in. 5 in. 560 in2 8 in. 490 in2 600 in 2 in. 440 in2 10 in. in
To find the surface area of the desing you need to find the are for all of the faces of the figure.
at the bottom we have a rectangular prism of sides 10, 10 and 2
sind the top, bottom and sides os this prism
[tex]\begin{gathered} \text{top and bottom} \\ 2\cdot10in\cdot10in=200in^2 \\ \text{sides } \\ 4\cdot10in\cdot2in^2=80in^2 \end{gathered}[/tex]total surface area at the bottom prism
[tex]200+80=280in^2[/tex]for the prism at the top we just add the area from the sides because the top was already considered at the top of the previous prism
[tex]\begin{gathered} \text{sides} \\ 4\cdot8in\cdot5in=160in^2 \end{gathered}[/tex]total surface are of the design is
[tex]280+160=440in^2[/tex]Answer to this question
Step-by-step explanation:
Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of pairs of socks and shorts because the socks now cost $6 a pair and the shorts cost $18.
a. Write a system of two equations that represents the number of pairs of socks and shorts bought each year.
b. How many pairs of socks and shorts did the team buy each year?
a. The system of equations to be solved is
5so + 17sh= 315
6so + 18sh= 342
b. The amount of pairs of socks and shorts bougth are 12 and 15 respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"so" is the pairs of socks bougth ."sh" is the amount of shorts bougth.You know that:
Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of pairs of socks and shorts because the socks now cost $6 a pair and the shorts cost $18.So, the system of equations to be solved is
5so + 17sh= 315
6so + 18sh= 342
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the unknowns in one of the equations and substituting the expression in the other equation.
In this case, isolating the variable "so" in the first equation, you obtain:
5so= 315 - 17sh
so= (315 - 17sh)÷5
so= 315÷5 - 17÷5sh
so= 63 - 17/5sh
Replacing this expression in the second equation you get:
6×(63 - 17/5sh) + 18sh= 342
Solving:
6×63 - 6×17/5sh + 18sh= 342
378 - 102/4sh + 18sh= 342
- 102/4sh + 18sh= 342 - 378
-12/5sh= -36
sh= (-36)÷ (-12/5)
sh= 15
Remembering that so= 63 - 17/5sh, you get
so= 63 - 17/5×15
so= 12
Finally, the amount of pairs of socks and shorts bougth are 12 and 15 respectively.
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A state lottery randomly chooses 4 balls numbered 1 though 43 without replacement. You choose 4 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values of n, p, and q and list the possible values of random variable x.
This is the hypergeometric not the binomial.
Difference between Binomial and Hypergeometric.Based on separate trials, a binomial random variable frequently models sampling with replacement. Based on non-independent trials, hypergeometric random variables frequently simulate sampling without replacement.
The hypergeometric distribution: When should we utilize it? It is employed when attempting to estimate the likelihood of attaining a specified number of successes from a particular sample size without replacement.
The number of times an event happens in a fixed number of trials is described by both the binomial distribution and the hypergeometric distribution.
Hence, we can say that this is the hypergeometric not the binomial.
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Jacki works at the mattress store and collects 4.9% commission on every mattress she sells. She had a big sales day today and ended up selling a total of $8948.96 worth of mattresses. How much commission will she make today?
Answer:438.499
Step-by-step explanation:4.9% of 8948.96(also calcuator)
At the local corner store, you can buy a 3-ounce bag of Nacho Cheese Doritos for $0.78 At Costco, you can get a larger 15-ounce bag of Nacho Cheese Doritos $3.75 Which is the better buy?
Work out 402.759 + 38.06?
Answer:
430.819
Step-by-step explanation:
If the m42 = 40, what is the m45?
Answer:
m5 = 140
Step-by-step explanation:
m1 = m2
m1 = 40
m5 + m1 = 180
m5 + 40 = 180
m5 = 140
A candle is 30 in. long. After burning for 12 min, the can- dle is 25 in. long. If it continues to burn at the same rate, how long will it take for the whole candle to burn?
72 min will take to burn 30 in. candle.
Divide the result by the number of burned hours after deducting the weight after the burn from the initial weight.
How to calculate time to burn candle ?On a scale, weigh the finished, unburned candle. Subtract the weight of the container if the candle is one with a container. This is the candle's original weight.
The candle should be lit and let to burn for four hours. Blow out the candle and let it cool completely after four hours. Remember to deduct the container's weight when weighing the candle once more. The weight after the burn is this.
We advise choosing grammes as your unit of measurement if your scale has a gramme measurement option. If you like, you can measure using ounces. You get numbers that are simpler to work with because grammes are a smaller unit of measurement.
Total length of candle = 30 in.
Time taken to 5 in. of candle burn = 12 min
Time take to burn 1 in = 12/ 5 = 2.4 min
How long will it take for the whole candle to burn = 2.4 * 30 = 72 min
72 min will take to burn 30 in. candle
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3 (a + b)solve ______= b for a c
First, apply distributive property:
[tex]\frac{3(a)\text{ + 3\lparen b\rparen}}{c}=b[/tex][tex]\frac{3a+3b}{c}=b[/tex][tex]3a+3b=bc[/tex][tex]3a\text{ = bc - 3b}[/tex]Common factor b
[tex]3a=b(c-3)[/tex][tex]a=\frac{b(c-3)}{3}[/tex]Two buses leave a station at the same time and travel in opposite directions. One bus travels 9 km/h slower than the other. If the two buses are 514 kilometers apart after 2 hours, what is the rate of each bus?
At the hardware store, a carpenter spent $100.00 on wood and $100.00 on tools. How much did he spend in all?
Answer: 200.00
Step-by-step explanation:
Am I reading it wrong? 100 + 100 = 200
100.00 + 100.00 is the same thing except with decimal points
Please help! Using the bar chart, what percent of the world population lives in Asia?
Answer:
58.25%
Step-by-step explanation:
add all the numbers
3340/all the numbers=your final answer
I need a tutor for Honors Geometry please! I am a Freshman!
Which of the following graphs has the smallest y-intercept and which graph would have the largest maximum as X moves towards 100?
Step 1
Given;
Step 2
[tex]\begin{gathered} y=1.3x \\ y-interecept\text{ is found when we set x=0} \\ y=1.3(0) \\ y-intercept=(0,0) \end{gathered}[/tex][tex]\begin{gathered} y=(1.3)^x \\ y=(1.3)^0 \\ y=1 \\ y-intercept=(0,1) \end{gathered}[/tex][tex]\begin{gathered} y=-0.8x+10 \\ y=-0.8(0)+10 \\ y=10 \\ y-intercept=(0,10) \end{gathered}[/tex][tex]\begin{gathered} y=10(0.8)^x \\ y=10(0.8)^0 \\ y=10 \\ y-intercept=(0,10) \end{gathered}[/tex]Thus,
[tex]y=1.3x\text{ has the smallest y-intercept}[/tex][tex][/tex]What is the equation for the following graph?option 1: y=1/2x+2option 2: y= -1/2x+2option 3: y=2x+2option 4: y= -2x+2
The Solution.
The equation of the given graph is an equation of a line, which is given as the formula below:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m = slope} \end{gathered}[/tex]First, we shall pick any 2 coordinates in the given line graph:
(-4,0) and (0,2)
[tex]\begin{gathered} (-4,0)\rightarrow(x_1=-4,y_1=0) \\ (0,2)\rightarrow(x_2=0,\text{ }y_2=2) \end{gathered}[/tex]The slope ( m) is given as below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the appropriate values given above, we get
[tex]m=\frac{2-0}{0--4}=\frac{2}{4}=\frac{1}{2}[/tex]So, the equation of the graph is :
[tex]\begin{gathered} y-0=\frac{1}{2}(x--4) \\ \\ y=\frac{1}{2}(x+4) \\ or \\ 2y=x+4 \end{gathered}[/tex]16. Find the measure of 2 ABC in circle D.a. 100A100b. 50C. 140d. 25
we have that
m by inscribed angle
so
mm
