Total amount in the account after 25 years is, $5,500.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
We have to given that;
Kimi Skuban deposits $2,000 at the beginning of each year.
The account pays 7% compounded annually.
Now, We know that;
⇒ Interest = PRT / 100
Where, P is principal amount, R is interest rate and T is time in years.
Substitute all the values, we get;
⇒ Interest = PRT / 100
⇒ Interest = 2000 × 7 × 25/ 100
⇒ Interest = $3,500
Hence, Total amount in the account after 25 years is,
⇒ $2,000 + $3,500
⇒ $5,500
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What is g(x)?
O A g(x)=-x
OB. g(x)=-lxi
OC. g(x)=-2*
O D. g(x)=-x²
Answer:
c.
Step-by-step explanation:
this graph is exponential equation
Fiona is purchasing hammers and wrenches for her workshop, and she would like to
spend under $120. Each hammer costs $5, and each wrench costs $6. Let x be the
number of hammers and y be the number of wrenches.
Select the inequality that describes the situation.
O 6x + 5y< 120
5x + 6y> 120
O6x + 5y 120
5x + 6y< 120
Answer:
The inequality that describes the situation is 5x + 6y < 120
Step-by-step explanation:
This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.
The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.
The other options:
6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.
5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.
6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.
Please help me with the blanks.
Each answer can be used more than once, by the way.
Simplificar -3+{4-2[6-3+4(5-7)]+3
Answer:
14
Step-by-step explanation:
Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).
1. Comience por simplificar la expresión dentro de los paréntesis.
4-2[6-3+4(5-7)]
4-2[6-3+4(-2)]
4-2[6-3-8]
4-2[-5]
4+10 = 14
2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:
-3+{14}+3
3. Ahora podemos sumar y restar de izquierda a derecha.
-3+14+3 = 14
Entonces, la expresión simplificada es 14.
Does anyonw know how to solve:
cos2a=4/5?
The value of a is 18.43°
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, cos2a=4/5
cos 2a = 4/5
2a = cos⁻¹(4/5)
2a = 36.86°
a = 18.43°
Hence, the value of a is 18.43°
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casey draws a rectangle array that is 1,167 units long and 7 units wide. what is the area of caseys array?
The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of
8169 square unitsHow to calculate the area of the rectangleThe formula for the area of a rectangle is the product of length and wide. This is written mathematically as
= length * wideness
In the problem the rectangular array made by Casey has a the following dimensions
length = 1167 units
wide = 7 units
Area of rectangle = length * wideness
substituting the values
Area of rectangle = 1167 * 7
Area of rectangle = 8169 square units
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A mother gives birth to a 7-pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y=mx+b that describes the baby's weight.
y =___________________
Answer:
y = 2/3 x + 7
Step-by-step explanation:
At birth represents the beginning of time for the baby. Lets call this month zero. So here are your coordinates.
x = 0 y = 7 ----> at birth
x = 3 y = 9
x = 6 y = 11
x = 9 y = 13
Now we find the slope between each point. Since the common difference of y is 2 and the common difference in x is 3 , the slope will be
slope = y / x = 2 / 3
Therefore, the equation of the line that represents this relationship is
y = (2/3) x + 7
A jailer carries a large key ring. The key ring has a diameter of 4 inches. What is the key ring's radius?
Answer:
2 inches
Step-by-step explanation:
The radius is simply the distance from the edge if you were at the center, which is equal to half the diameter. So given the diameter is 4 inches, we divide that by two, [tex]\frac{4\text{ inches}}{2}=2\text{ inches}[/tex] and that's our radius!
I have 18 students that took a test. 4 of the students passed. What is the percentage of the students that passed and the students that didn't pass?
Step-by-step explanation:
as always with % calculations :
first find what is 100% or 1%. everything else can be calculated from that.
in our case, we got 100% = 18.
therefore, 1% = 100%/100 = 18/100 = 0.18
how many % are 4 students ?
as many as the times 1% (0.18) fits into 4 :
4 / 0.18 = 22.22222222... %
so,
22.22222222... %
of the students passed.
therefore,
100 - 22.22222222... = 77.77777777... %
of the students did not pass.
help with this please
Answer:
B
Step-by-step explanation:
The numbers are the same so they would be on the same place on the number line.
Answer:
If A = B, where on the number line will A appear?
The correct answer is B. In exactly the same location as B.
This is because when we say A = B, it means that A and B have the same value, meaning they are located in the same place on a number line.
The range of a set of numbers is 16.
The minimum value is 6.
What is the maximum value?
Answer:
22
Step-by-step explanation:
Range : Maximum - Minimum
Minimum = 6
Maximum = A (Let maximum be A)
Hence,
16 = A - 6
A = 22
Maximum = 22
Hi can someone help me do this math problem? How would you do it in a ti-84 calculator or by hand?
The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.
b. -2
What is an imaginary number?An imaginary number is a number which is obtained by finding the square root of a negative number.
The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]
Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;
[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]
[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]
Where x is real, for the number to be purely an imaginary number, we get;
[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]
[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]
Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;
x + 2 = 0
x = 0 - 2 = -2
x = -2
The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2
The correct option is; b. -2
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Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answer:
D
Step-by-step explanation:
Are the two triangles below similar? If so, write a similarity statement, and stay with similar to criteria can be used to prove it.
Similarity statement-
1. PNK DKG
2. PNK GDK
3. PNK KGD
4. The triangles are not similar
Criteria-
1. AA
2. SAS
3.SSS
4. Not applicable, the triangles are not similar
The two triangles below show the property of similarity.
The first property is the Side.
The side PN is similar to the side DG.
The second property his angle.
∠PNK = ∠DGK = 90°
The third property would be side as well.
Side NK is similar to the side GK.
Thus, the two triangles are similar.
Similarity is the mathematical property of triangles, wherein two triangles are called similar if they have either two congruent angles and one similar side, or two similar sides in ratio with one another and a congruent angle.
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The perimeter of an isosceles triangle is 32.7 inches. The length of its base is 9.5 inches. Find the length of each of the other two identical sides.
Answer:
1.72 inches
Step-by-step explanation:
= P=2s×b
= 32.7=2s×9.5
= 32.7=19s
= 32.7/19=19s/19
= s=1.72
A manufacturing firm want to determine the proportion of defects in a manufacturing process. How many of its products does it need to sample if it wants to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%?
The firm needs to sample 138.297 products to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%.
What is a manufacturing firm?Generally, To determine the sample size needed to achieve a ±5% accuracy at a 95% confidence level, with a maximum expected proportion of defects of 10%, you can use the formula for sample size for a proportion. The formula is:
n = (z^2 * p * (1-p)) / E^2
Where:
n is the sample sizez is the standard normal deviate corresponding to the desired level of confidence (1.96 for a 95% confidence level)p is the maximum expected proportion of defects (0.10 in this case)E is the margin of error (0.05 in this case)Plugging in the given values, we get:
n = (1.96^2 * 0.10 * (1-0.10)) / 0.05^2
n =138.297
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At noon, a 36 foot building casts a 20 foot shadow. Find the shadow cast by a 6 foot tree. Set up a proportion and solve. Be sure to show all your work!
Answer:
3 1/3 ft
Step-by-step explanation:
Let SHADOW and HEIGHT pertain to the building, and let shadow and height pertain to the tree.
The proportion is:
HEIGHT/SHADOW = height/shadow
Now we fill in with the numbers we know, and "shadow" for the shadow of the tree.
(36 ft)/(20 ft) = (6 ft)/(shadow)
Cross multiply.
36 × shadow = 6 × 20
36 × shadow = 120
shadow = 120/36 = 10/3
shadow = 3 1/3
Answer: 3 1/3 ft
Jonathan Rodero operates a booth selling T-shirts during concerts. Following each event, he makes : deposit to his savings account. Today he has checks: $40.00, $50.00, and $35.00; cash and coins: 8 fifty-dollar bills. 12 twenty-dollar bills, 12 ten-dollar bills, 8 five-dollar bills, 22 one-dollar bills; less $100 in cash.
Jonathan deposited $847 in his saving account.
What is deposit slip?This bank deposit slip is the record of the total amount that a person is depositing into a bank account. It includes the details of the items being deposited, that is, the number of checks and notes or coins of each type in the form of cash.
Given,
Amount in checks = $40 + $50 + $35 = $125
8 fifty-dollar bills = 8 × $50 =$400
12 twenty-dollar bills = 12 × $20 = $240
12 ten-dollar bills = 12 × $10 = $120
8 five- dollar bills = 8 × $5 = $40
22 1-dollar bills = 22 × $1 = $22
Subtotal = $125 + $400 + $240 + $120 + $40 + $22 = $947
Less cash = $100
Total = $947 - $100
Total = $847
Hence, $847 is the total deposited amount by Jonathan.
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evaluate -
[tex]\int \:{tan}^{ - 1} x \: dx[/tex]
tysm! :)
What is 1% of 800?
Hint: We can think of 1% as a common fraction.
Reason:
1% converts to the decimal form 0.01
0.01*800 = 8
Basically we move the decimal point two spots to the left
So the 800.0 becomes 8.000 or simply 8
Answer:
8
Step-by-step explanation:
Anything in percentage format can be expressed as a fraction by dividing by 100
Thus
[tex]\textrm{1\% }= \dfrac{1}{100}[/tex]
1% of 800 is found by multiplying 800 by the above fraction
[tex]\textrm{1\% of 800 } = 800\cdot \dfrac{1}{100} = 8[/tex]
Pleaseeeeew i beg you
. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
volume of the cylinder.
Solve the equation
4sinxcosx^2 - 1 = 2cos(sin x - 1)
Answer:
Step-by-step explanation:
To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:
2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)
We can then substitute this expression on the left-hand side of the original equation and simplify:
4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)
Rearranging terms, we have:
4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1
We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:
4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1
Simplifying further:
4sinxcosx^2 - (cosx)cos(1) = 1
Now we can divide both sides by cos(1):
4sinxcosx^2/cos(1) - cosx = 1/cos(1)
Rearranging terms:
cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:
(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
We can then divide both sides by (4sinxcosx^2/cos(1) - 1):
2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)
And finally, we can solve for cosx:
cosx = 1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)
This is the solution to the equation.
simplify 7m-2(3m^2 +mn)
Answer: 7m-6m²-2mn
Step-by-step explanation:
Multiply each term in parenthesis by -2
Calculate product (2x3=6)
7m-6m²-2mn
Sally bought a soft drink for $3 and seven candy bars. she spent a total of $31. how much did each candy bar cost? Write an equation to represent the problem, and show the steps to solve it.
Answer:
31=3+x
31=-3+x
28=x
28/7
$4
Each Candy bar cost $4 each
Step-by-step explanation:
A cookie factory uses 3 3/4 bags of flour in each batch of cookies. The factory used 7 1/2 bags of flour yesterday. How many batches of cookies did the factory make?
Answer:
To find out how many batches of cookies the factory made, we need to divide the total amount of flour used (7 1/2 bags) by the amount of flour used per batch (3 3/4 bags).
We can start by converting 7 1/2 bags of flour to a mixed number: 7 1/2 bags = 7 + 1/2 = 7.5 bags
Next, we can convert 3 3/4 bags of flour to a mixed number: 3 3/4 = 3 + 3/4 = 3.75 bags
Then, we can divide the total amount of flour used by the amount of flour used per batch:
7.5 bags / 3.75 bags/batch = 2 batches
Therefore, the factory made 2 batches of cookies yesterday
A track runner counted the number of races he had during a season. The graph shows the relationship between the number of track meets, x, and the number of races, y.
coordinate plane with the x axis labeled number of track meets and the y axis labeled number of races with a line that passes through the points 0 comma 5 and 1 comma 7
Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points)
Part B: What does the slope mean for the relationship between the number of races and the number of track meets? (3 points)
Part C: Interpret the y-intercept in the situation. (3 points)
Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows:
y = 2x + 5.
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How much is 9.6 KB kilobytes
9.6 KB kilobytes is equal to 0.0096 MB
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
1kB=1000 bytes
1MB=1000 KB
1kB=1/1000MB=0.001 MB
9.6 KB is nothing but 9600 bytes
9.6 KB in MB we have to convert
Now multiply 9.6 with 0.001
9.6×0.001
0.0096 MB
Hence, 9.6 KB kilobytes is equal to 0.0096 MB
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calculate 76.7 × 308.2 ÷ 8.04
Answer:
Step-by-step explanation:
2940.1667
Answer:
2940.16667
Step-by-step explanation:
A survey was given to a random sample of 75 voters in the United States to ask about their preference for a presidential candidate. Of those surveyed, 36% of the people said they preferred Candidate A. At the 95% confidence level, what is the margin of error for this survey expressed as a percentage to the nearest tenth? (Do not write
±
±).
The margin of error for this survey is 8% (0.08*100) rounded to the nearest tenth.
What is the margin of error?
The margin of error is a measure of the precision of a sample estimate. It is used to indicate the degree of uncertainty associated with a sample estimate.
The formula to calculate the margin of error at the 95% confidence level for a sample proportion is:
Margin of error = z* √(p*(1-p)/n)
Where:
z is the z-score for the 95% confidence level (1.96)
p is the sample proportion (36%)
n is the sample size (75)
So the margin of error for this survey would be:
Margin of error = 1.96 * √((0.36 * (1 - 0.36)) / 75)
Margin of error = 0.08
Hence, the margin of error for this survey is 8% (0.08*100) rounded to the nearest tenth.
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