Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.
Interest is calculated by multiplying the rate with the principal.
Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.
We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000
Now we can write the necessary equation to solve for x.
or, 0.13x+0.03(60000-x) = 5000
or, 0.13x+1800-0.03x = 5000
or, 0.1x+1800 = 5000
or, 0.1x = 3200
or, x = 32000
So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.
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The population of Nevada was 3.0 million in 2018 and 2.7 million. in 2010. Assuming an exponential model: (a) Write the population of Nevada in the form N = Noat, where N is the population of Nevada in millions, No and a are constants, and t is time in years since 2010. NOTE: Enter the exact answer for No. Enter an exact value for a or round to 4 decimal places. N(t) = = (b) What was the estimated population of Nevada in 2009? NOTE: Round your answer to 3 decimal places. The population in 2009 was approximately million people.
the exponential model is given as N = 2.7 (1.0133)^(t) and the estimated population in 2009 was 2.6646 million.
According to the question, we have the information that:
N = 3 million
No = 2.7 million
a = 8 years
Now, we need to find the exponential model for the given data.
Do putting the values in the equation to get the value of a, we have:
3 = 2.7 (a)^(8)
1.1111 = a^(8)
a = 1.0133
So, the exponential model will be:
N = 2.7 (1.0133)^(t)
Now, the estimated population in 2009 will be:
t = - 1
So, we get that:
N = 2.7 (1.0133)^(-1)
N = 2.7 / 1.0133
N = 2.6646 million
Therefore the exponential model is given as N = 2.7 (1.0133)^(t) and the estimated population in 2009 was 2.6646 million.
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Write the standard form of the equation of the circle with the given characteristics.
Center: (-3, 4); Radius: 3
4. [-/6 Points]
DETAILS
LARPCALC11 1.3.027.
Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.)
(-8, -12), (1, 24)
The standard form of the equation of the circle is (x+3)²+(y-4)²=9 .
The slope of the line is
A circle is defined as the locus of a moving point which is always equidistant from a given point.
This given point is called the center of the circle.The distance between the center and the circumference of the circle is the radius if the circle.The standard form of a circle is given by the equation : (x-x₁)²+(y-y₁)²=r² , where (x₁,y₁) is a point on the circle and r is the radius.The given point on the circle is (-3, 4) and the radius is 3 units.
Hence the standard form of the equation of the circle is :
(x-{-3})²+(y-4)²=3²
or, (x+3)²+(y-4)²=9
Let the two given two points as A(-8, -12) and B(1, 24).
Now the slope of the line AB can be calculated by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]
Now let us put the given values in the equation to calculate slope:
[tex]m_{AB}=\frac{24-(-12)}{1-(-8)}\\\\or, m_{AB}=\frac{36}{9} \\\\or, m_{AB}=4[/tex]
Hence the slope of the line is 4.
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the patter is 1, 8, 27, 64, 125 if this patter was produced in a normal spreadsheet what is the number in cell A14?
The number in cell A14 is 2744
How to determine the number in cell A14?The pattern is given as
1, 8, 27, 64, 125
When the above number in the pattern is represented as exponents, we have
1^3, 2^3, 3^3, 4^3, 5^3
So, the nth term is
Tn = n^3
In cell A14, the value of n is 14
So, we have
T14 = 14^3
Evaluate
T14 = 2744
Hence, the number in cell A14 is 2744
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26) Jody earns $8.00 per hour.
Michael earns $10.00 per hour.
They each earn a 2% commission on what they sell.
Jody sold $6000. She worked 30 hours.
Michael sold $5000. He worked 40 hours.
What were each of their earnings for the week?
What was the difference in their earnings?
Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference between their earning is $140
Jody sold $6000
2% commission of $6000 is (2/100)x 6000
Jody's commission is $120
He earns $8 per hour and he worked for 30 hours
= 8 x 30
=$240
Jody's total earning = 240 + 120 = $360
Michael sold $5000
2% commission of $5000 is (2/100)x 5000
Michael's commission is $100
He earns $10 per hour and he worked for 40 hours
= 10 x 40
=$400
Michael's total earning = 400 + 100 = $500
Difference in there earnings= Michael's earning - Jody's earning
= 500- 360
= $140
Therefore, Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference in their earning is $140
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Simplify negative 2 and 3 over 5 minus 6 and 2 over 7.
The value of the expression is -311/35
How to simplify the expression?The expression is given as
negative 2 and 3 over 5 minus 6 and 2 over 7.
Rewrite properly as
- 2 3/5 - 6 2/7
Express as improper fraction
-13/5 - 44/7
Take the LCM
(-13 * 7 - 44 * 5)/35
Evaluate
-311/35
Hence, the value of the expression is -311/35
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one driver had lap speeds of 195.3 mph, 190.456 mph,193.557 mph, and 192.575 mph. What was the driver's average speed for the laps driven?
The driver’s average speed for the laps driven is 192.972mph
The formula for average speed is given below:
Average speed = (Sum of the lap speeds driven by the driver) / (Total number of the lap speed driven by the driver)
Sum of the lap speed = 195.3 + 190.456 + 193.557 + 192.575 mph
= 771.888 mph
Number of lap speed driven by the driver = 4
Now putting the required values in the formula of average speed we get
Average speed = 7771.888/4 mph
= 192.972 mph
Hence the driver’s average speed for the laps driven is 192.972mph
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What is the answer to this help (number 4.)
What is the circumference of a radius equals 6 inches
The circumference of a radius equals 6 inches is 37.68 inches
What is the circumference of a radius equals 6 inches?The radius is given as
r = 6 inches
The circumference of a circle is calculated as
C = 2pi r
So, we have
C = 2 * 3.14 * 6 inches
Evaluate the product
C = 37.68 inches
Hence, the circumference of a radius equals 6 inches is 37.68 inches
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f(x) = 3x - 4
Find f(-1)
Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.
complementary angles m < DFG = 48, m < JKL = 42 is value of x .
What is the opposing angle to the above example?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So m < DFG < + m < JKL = 90
Now replace the expressions and solve for x
x + 5 +x - 1 =90
2x + 4 = 90
2x = 90 - 4
2x = 86
x = 43
Now replace x with 43 and find out each angle
m < DFG = x + 5
m < DFG = 43 + 5 = 48
m < DFG = 48
m < JKL = x - 1 = 43 - 1 = 42
m < DFG = 48
m < JKL = 42
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I need help on question 1-6 please
Ill mark brainlist
Answer:
1: 7.2 2: 2012 3: 2014 and 2015 4: 2011 5: 6.6 6:1
Step-by-step explanation:
I don't have time to explain.
It just is.
please refer to the image
a. Solve x + 8 - x + 8
b. If you simplify an equation and get 00, what can you conclude about the solution(s) of the original equation?
To solve an linear equation we need to use BODMAS rule.
Here the given equation is;
(x+8-x+8)
We know very well that if two like numbers have opposite sign and are added then it gets cancelled and gives zero as the result.
Similarly, here x and -x gets cancelled and we get 16 as the result.
If we get the solution of an equation as zero then we may say that the equation has no real solution. That means there are no values of the unknown which will complete the equation.
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Given −16.98(5.2), find the product.
−882.96
−88.296
−15.282
11.886
Answer: 882.96
Step-by-step explanation:
The product of -16.98 and 5.2 is -88.296.
The given expression is -16.98 multiplied by 5.2. To find the product, multiply the two numbers:
-16.98 * 5.2 = -88.296.
Therefore, the product of -16.98 and 5.2 is -88.296. The correct answer is -88.296, which matches the second option. When multiplying a negative number by a positive number, the result is negative. The calculation involves multiplying the absolute values (16.98 and 5.2) and then assigning the negative sign to the product. In this case, the product is -88.296, as it accurately represents the multiplication of -16.98 and 5.2.
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a repair bill for your ebike is $188. the parts costs $73 dollars and the cost of the labor is $46 per hour.
a. write an equation that represents this situation.
b. how many hours dud the repair take?
Answer:
188 = 46x + 73
It took 2 1/2 or 2.5 hours to complete.
Step-by-step explanation:
There is a one time cost of 73 for the parts, but the hours will be 46 per hour. I know the total cost, so we need to solve for x which is the hours.
188 = 46x + 73 Subtract 73 from both sides of the equation
115 = 46x Divide both sides of the equation by 46
2.5 = x
Translate this sentence into an equation.
The difference of Goran's height and 10 is 57
Use the variable g to represent Goran's height.
Answer:
g-10=57
Step-by-step explanation:
'Difference' means to subtract.
Find the union of the sets (22, 33, 44, 55) and (66, 44, 22}
Application of Finite Mathematics
The union of the sets is { 22, 33, 44, 55, 66 }
What is the union of sets?The union of sets can be defined as the sum of the elements of two or more sets without repetition of those elements.
It is also known as the combination of the all the elements of two or more sets.
It is denoted using the symbol , ' ∪ '
Given the sets;
(22, 33, 44, 55)(66, 44, 22}The union of the sets is:
{ 22, 33, 44, 55, 66 }
Thus, the union of the sets is { 22, 33, 44, 55, 66 }
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A rectangle's width is 6 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
A. A(1)=1²-61
B. A(7)=7w
c. A(1)=12+61
D.A(7)=1-6
Answer:
A. A(l) = l² -6l
Step-by-step explanation:
You want a quadratic function for the area of a rectangle whose width is 6 feet less than its length.
Rectangle areaLet l (ell) represent the length of the rectangle in feet. Then the width will be 6 feet less, or (l -6). The area is the product of length and width:
A = LW
A(l) = l(l -6)
A(l) = l² -6l . . . . . . use the distributive property to eliminate parentheses
At the visitor center gift shop Peter can afford to buy either 4 postcards and 9 stickers or 8 postcards and 6 stickers both options leave him no change if Peter wanted to buy only postcards how many could he buy
Answer:
20
Step-by-step explanation:
Hope the picture helps
You keep subtracting until you get zero and you keep adding the same amount
If Peter wanted to buy only postcards, he could buy 2 postcards.
Given that,
Peter can afford to buy either 4 postcards and 9 stickers or 8 postcards and 6 stickers.
Both options leave him with no change.
Peter wants to buy only postcards.
Assume that the cost of a postcard is the same as the cost of a sticker.
In the first scenario,
Peter spends the same amount on postcards and stickers.
So, if he wanted to buy only postcards,
He could buy half the number of postcards he could buy in the first scenario.
Therefore, Peter would be able to buy 2 postcards if he wanted to buy only postcards.
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solve for b r=9(b+a)
What is the sum of the two polynomials?
x² - 4x +5
+3x²+x-2
O 4x4 - 3x² +3
O 4x²-3x +3
O 4x²-3x+7
O 3x²-3x+7
O 3x²-3x +3
Answer:
4x^2-3x+3 yessssssssssss
You bought f pounds of fruit today. Today, you bought 3 times as many pounds of fruit as you bought yesterday. Which expression correctly shows how many pounds of fruit you bought yesterday? is it
f + 3
3f
3 ÷ f
f ÷ 3
or
none of the above
The answer would be 3f.
Suppose these show number of hours each student in a class slept last night:
8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6
What is the mean of these numbers (rounded to the nearest tenth)?
What is the median?
Mean: 6.9 hours; Median 7 hours
Mean: 6.9 hours; Median 7.5 hours
Mean: 7 hours; Median 6.9 hours
Mean: 7.2 hours; Median 7 hours
⊂ Hey, rosedalphinis ⊃
Answer:
Mean: 6.9 hours; Median 7 hours
Step-by-step explanation:
⇒ Given:
-------------------------------------------------------------------------------------------------------------
Suppose these show number of hours each student in a class slept last night:
8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6
What is the mean of these numbers (rounded to the nearest tenth)?
What is the median?
Mean: 6.9 hours; Median 7 hours
Mean: 6.9 hours; Median 7.5 hours
Mean: 7 hours; Median 6.9 hours
Mean: 7.2 hours; Median 7 hours
-------------------------------------------------------------------------------------------------------------
⇒ Solution~:
-------------------------------------------------------------------------------------------------------------
Let's first define "Median".
You may be wondering "What is median/What is mean?".
When it asking for "Mean" It asking for the average.
When it asking for "Median" It asking for the middle number.
The formula for "Mean" is : M = sum of the terms/number of terms
According to the given we have;
8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6
Let's first find the "Mean":
First, add all the number together.
8 + 4 + 8 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6
12 + 8 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6
20 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6
27 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6
34 + 9 + 6 + 5 + 10 + 7 + 6 + 6
43+ 6 + 5 + 10 + 7 + 6 + 6
49+ 5 + 10 + 7 + 6 + 6
54+ 10 + 7 + 6 + 6
64 + 7 + 6 + 6
71+ 6 + 6
77 + 6
= 83
Now let's count how many numbers of hours each student in a class slept.
8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6 = 12
Now 83 divide by 12:
83/12 = 6.9166666666667 {Round}
6.9166666666667 = 6.9
Therefore, Mean = 6.9
-------------------------------------------------------------------------------------------------------------
Next, Let's find the "Median":
To find the Median, place the numbers in value order and find the middle.
⇒ 8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6
⇒ 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
Now we have them in order:
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
Then, we find the middle number:
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10
Now You see that there two's 7 left.
If there is an even number of numbers add the two middles and divide by 2
Thus,
7 + 7 = 14
14/2 = 7
Therefore, Median = 7.
-------------------------------------------------------------------------------------------------------------
According to the solving above we can conclude that:
Mean: 6.9 hours; Median 7 hours
-------------------------------------------------------------------------------------------------------------
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HELP NOWWW!!!!! PLEASE
Question content area top Part 1 The coordinates of point T are (0,6). The midpoint of is (4,-6). Find the coordinates of point S. Question content area bottom Part 1 The other endpoint is enter your response here. (Type an ordered pair.)
Answer:
The end point is (8,-18)
Step-by-step explanation:
Whats 9,999 - 999 x (12 - 9) divided by 10?
Answer: 9699.3
Step-by-step explanation:
?
Part of a multiplication table is shown.
15 20 25 30
18
30 36
21
35 42
24 32 40 48
What two numbers are needed to complete the pattern in
the multiplication table?
OA) 21 and 24
OB) 24 and 24
OC) 24 and 28
OD) 21 and 28
The correct option is C) 24 and 28 for the given multiplication table.
What is defined as the multiplication table?The multiplication table (already known as the time's table) provides multiples of numbers. Multiplying a number by a set of whole numbers yields the multiplication table.The given multiplication are-
15 20 25 30This is the table 5 starting with;
5×3 = 15 ....... 5×6 = 30
18 __ 30 36This is the table of 6 starting with;
6×3 = 18 ....... 6×6 = 36
Thus, the missing number is;
6×4 = 24
21 __ 35 42This is the table 7 starting with;
7×3 = 21 ....... 7×6 = 42
Thus, the missing number is;
7×4 = 28
24 32 40 48This is the table of 8 starting with;
8×3 = 28 ....... 8×6 = 48
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The correct question is-
Part of a multiplication table is shown.
15 20 25 30
18 __ 30 36
21 __ 35 42
24 32 40 48
What two numbers are needed to complete the pattern in
the multiplication table?
OA) 21 and 24
OB) 24 and 24
OC) 24 and 28
OD) 21 and 28
What kind of passenger be considered a true negative ?
Answer: A someone with dangerous material passed by security
Step-by-step explanation:
I can't understand,
Answer:so dividing you add a extra zero behind the dot or point while multiplying you decrease the decimal to a whole number
if it is right pls give me brainliest
Step-by-step explanation:The relationship between 0.8 divided by 10^2 and 0.8x10^2 is that 0.8 divided by 10^2 means you add extra zero to the dot like this 0.008 so what it mean is that 10^2 is to add extra zeros in front of the point or dot in 0.8 while 0.8x10^2 decreases the zero like this 80 so we remove the 0 in 0.8 which mean 0.8 is no longer a decimal but a whole number now and then add a extra zero because 10^2 mean add two zeros so if you see a number infornt of 10^ like 2 is how many zeros you add. so you add to extra zeros to 0.8 which decreases
How to solve math problem
Answer: by doing math
Step-by-step explanation:
4. Plans to vote
“yes” on issue Q
Plans to vote
“no” on issue Q Total
Plans to vote
“yes” on issue P 8 12 20
Plans to vote
“no” on issue P 14 16 30
Total 22 28 50
The table above shows a survey of 50 registered voters
in a city. Each voter was asked whether they planned to
vote “yes” or “no” on two different issues. If a voter who
plans to vote “yes” on issue P is randomly selected, what
is the probability that voter also plans to vote “yes” on
issue Q
The probability that voter also plans to vote “yes” on issue Q is found to be 0.4.
What is defined as the probability?The ratio of the total count of favorable outcomes to a total number of outcomes like an event is defined as probability. The number of favorable outcomes for an experiment with 'n' outcomes is denoted by x.The following equation is used to determine the probability of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes
Probability(Event) = x/n
Eight voters intend to vote "yes" on both issues.
So, the favourable outcome becomes = 8.
Twenty voters intend to vote "yes" on issue P.
Thus, the total outcome = 20.
This is denoted by 8 /20 = 0.4.
Therefore, the likelihood that a voter will vote "yes" on issue Q is found to be 0.4.
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