Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
We have,
To determine which savings account has more money after 9 years, we can evaluate the amount of money in each account using the given equations.
For Savings Account A, the equation is:
A = 21.09t + 1125
Substituting t = 9 (since we're interested in the amount after 9 years), we get:
A = 21.09(9) + 1125 = 1300.81
So, after 9 years, Savings Account A will have $1300.81.
For Savings Account B, the equation is:
A = 1125(1 + 0.01875/2)^(2t)
Substituting t = 9, we get:
A = 1125(1 + 0.01875/2)^(2(9)) = 1318.98
So, after 9 years, Savings Account B will have $1318.98.
Therefore,
Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
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ng Linear Equations Using Similar Triangles On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7. Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3). What is the ratio of the rise to the run in the smaller triangle in the diagram? What is the ratio of the rise to the run in the larger triangle in the diagram? What is the equation of the line in slope-intercept form?
Answer:
Step-by-step explanation:
Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.
Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25
What is the future value of $1500 invested for 8 years at a continuously
compounding rate of 9% ?
Find the volume of this sphere.
Use 3 for T
8 in
V ≈ [?]in³
V = πr3
The volume of this sphere is 1607. 68 in³
How to determine the volumeIt is important to note that the formula that is used to calculate the volume of a sphere is expressed as;
V = 4/3 πr3
Given that the parameters are;
V is the volume of the sphereπ takes the constant value of 3.14r is the radius of the sphereFrom the information given,
Substitute the values, we have;
Volume = 4/3 × 3.14 ×8³
Find the cube values, we get;
Volume = 4/3 × 3.14 × 512
Multiply the values
Volume = 2143. 57 in³
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is the p- value 4.91541E-15 higher or lower than 0.05?
The p-value of 4.91541E-15 (or 4.91541 x 10^-15) is considerably beneath the conventional significance level of 0.05 employed in statistical hypothesis testing.
How to get the p value that is greaterIn hypothesis testing, the p-value symbolizes the probability of detecting the test statistic (or an even larger value) under the null hypothesis. A p-value of 0.05 or below often appears statistically relevant, suggesting powerful evidence contrary to the null hypothesis.
Therefore, a p-value of 4.91541E-15 being far less than 0.05 implies very compelling evidence against the null hypothesis.
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please find the area with the formula or how you found the anwser use link below
The equivalent expression for 8y + 12 + 2y + 8 will be 10y + 20.
The number of problems that she get wrong is 4.
The days that Jared work to make 20 bird houses is 15 days.
How to calculate the valueThe equivalent expression for 8y + 12 + 2y + 8 will be:
= 8y + 12 + 2y + 8
= 10y + 20
The number of problems that she get wrong is:
= (1 - 84%) × 25
= 0.16 × 25
= 4.
The days that Jared work to make 20 bird houses is:
= 3/4 × 20
= 15 days.
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Write an equivalent expression for 8y + 12 + 2y + 8
Maria’s math test had 25 questions. She got 84% correct. How many problems did she get wrong?
Jared made 4 bird houses in 3 days. How many days will Jared work to make 20 bird houses?
The cost of a first-class postage in 1970 was $0.06 and in year 2013 was $0.46. Determine the average annual rate of increase in the price of postage stamps during the
years 1970 to 2013.
A. 18.47%
B. 4.851%
C. 6.63%
D. 4.84%
From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.
The formula for compound interest is:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.
In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.
Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.
Then, we can write:
[tex]A = P(1 + r)^t[/tex]
Substituting the values, we get:
[tex]0.46 = 0.06(1 + r)^{43[/tex]
Dividing both sides by 0.06, we get:
[tex]7.67 = (1 + r)^{43[/tex]
Taking the 43rd root of both sides, we get:
[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]
Subtracting 1 from both sides, we get:
r = 0.04851 = 4.851%
Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.
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The function A = A0e
-0.0077x models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault. If
300 pounds of the material are initially put into the vault, how many pounds will be left after 140
years
There will be about 105.28 pounds of radioactive material in the concrete vault after 140 years.
The function [tex]A = A_0e^{(-0.0077x)}[/tex] gives the amount A of the radioactive material, where A0 is the initial amount of the material, x is the number of years since it was put in the vault, and e is the mathematical constant approximately equal to 2.71828.
We are given that the initial amount of material put into the vault is 300 pounds.
Therefore, [tex]A_0 = 300[/tex].
We want to find the amount of material that will be left after 140 years. Therefore, x = 140.
Substituting these values into the function, we get:
[tex]A = A0e^{(-0.0077x)}\\A = 300e^{(-0.0077 * 140)}\\A = 105.28[/tex]
Therefore, after 140 years, approximately 105.28 pounds of radioactive material will be left in the concrete vault.
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Summary of Angle Relationships in a Circle
The summary of Angle Relationships in a Circle is given.
The following is an overview of angle relationships in a circle:
The vertex of a central angle is the center of the circle. A central angle's length equals the length of the arc it crosses.
Inscribed angle: An angle with a circle as its vertex and sides that intersect two separate arcs. An inscribed angle has half the length of the arc it intersects.
Tangent-chord angle: A tangent-chord angle is generated when a tangent and a chord cross at the point of tangency. The length of this angle is half the length of the intercepted arc.
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Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day. Which equation or inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks?
The inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks is 50 ≥ 3.5x + 5
We are given that Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day.
We need to find the equation or inequality that represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks.
Sydney started with zero money in her piggy bank and adds $3.50 each day means 0 + 3.50 and Destiny started with $50 in her piggy bank and spends $5 of her money each day then
the inequality becomes as ;
50 ≥ 3.5x + 5
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Given the following equation, x^4 -4x^2+10x+13 use synthetic division and show if they are root or not.
Please show steps.
The zeros are not the factors of the expression using the synthetic method
Testing the factors using the synthetic methodThe expression is given as
x⁴ - 4x² + 10x + 13
Testing the factors, we have
(x, y) = (2, 0)
The synthetic set up is
2 | 1 0 -4 10 12
|__________
Bring down the first coefficient, which is 1 and repeat the process
2 | 1 0 -4 10 12
|___2_4__0__20__
1 2 0 10 32
This has a remainder of 32
So, (2, 0) is not a factor
(x, y) = (1, 0)
The synthetic set up is
1 | 1 0 -4 10 12
|__________
Bring down the first coefficient, which is 1 and repeat the process
1 | 1 0 -4 10 12
|___1__1__-3_7__
1 1 -3 7 19
This has a remainder of 19
So, (1, 0) is not a factor
(x, y) = (-1, 0)
The synthetic set up is
-1 | 1 0 -4 10 12
|__________
Bring down the first coefficient, which is 1 and repeat the process
-1 | 1 0 -4 10 12
|__-1__1__3__13__
1 -1 -3 13 25
This has a remainder of 25
So, (-1, 0) is not a factor
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What is the probability that either event will occur?
14,24,10,18
P(A or B)= ?P(A)+P(B)-P(A and B)
Please answer in a simple way so I can understand how to do it.
The probability that either event will occur to the nearest hundredth would be = 0.9
How to calculate the probability of the given events?To calculate the probability of the given events, the sample space should be generated and followed by the probability of each sample space generated.
That is;
P(A) = 14/18 = 0.78
P(B) = 10/18 = 0.56
P(A and B) = 0.78×0.56 = 0.4368
Therefore ;
P(A or B)= 0.78+0.56-0.4368
= 1.34- 0.4368
= 0.9
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lina bought two patio chairs that cost $ 37 each and a table that cost $ 58. what is the total cost of these items?
answer 95 I think that is the answer do you know it it is hard
Answer:
Total cost = $132
Step-by-step explanation:
We can find the total cost using the formula
total cost = (item 1 quantity * cost) + (item 2 quantity * cost)
We essentially find the sum of the product of item quantity and cost for each item:
Thus, for 2 chairs costing $37/chair and 1 table costing $58/table, the total cost is:
Total cost = (2 * $37) + (1 * $58)
Total cost = $74 + $58
Total cost = $132
Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks).
Graph this density curve.
Find the proportion of babies born after the 40th week of the year
Find the proportion of babies born before the 10th week of the year
Find the proportion of babies born between the 10th and 40th week of the year
The proportion of the babies born
After the 40th week of the year: 80.7%Before the 10th week of the year: 12.9%Between the 10th and 40th week of the year: 67.8%Finding the proportion of babies bornGiven that
Uniform Distribution from 1 – 53
This means that
a = 1 and b = 53
So, we have
Mean = (a + b)/2 = (1 + 53)/2 = 27
Standard deviation = √[(b – a)² / 12] = √[(53 – 1)² / 12] = 15
After the 40th week of the year
The z-score is calculated as
z = (x - mean)/Standard deviation
So, we have
z = (40 - 27)/15 = 0.8667
So, we have
Proportion = P(z > 0.8667)
Proportion = 80.7%
Before the 10th week of the year
z = (10 - 27)/15 = -1.133
So, we have
Proportion = P(z < -1.133)
Proportion = 12.9%
Between the 10th and 40th week of the year
This is calculated as
Proportion = (-1.133 < z < 0.8667)
So, we have
Proportion = 67.8%
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What is the volume? round to nearest thousandth
The volume of the cone is 37.70 cm³.
What is the volume of the cone?The volume of the cone is calculated as follows;
V = ¹/₃πr²h
where;
r is the radius of the coneh is the height of the coneThe radius of the cone is calculated by applying the following formula;
r = √ (5² - 4²)
r = 3 cm
The volume of the cone is calculated as;
V = ¹/₃πr²h
V = ¹/₃π(3)²(4)
V = 37.7 cm³
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Edgar has several different types of songs in a playlist. Suppose he plays a song at random from the playlist. How much greater is the probability that he plays a rock song than a hip hop song
The probability that he plays a rock song than a hip hop song is greater than 0.1. The Option B is correct.
How much greater is the probability?Probability helps to find out the likelihood of the occurrence of an event by measuring the chance of an event happening and is equal to the number of favorable events divided by the total number of events.
Given that:
Total of songs = 40
Prob (playing rock) = 15/40
Prob (playing hip-pop) = 11/40
How much greater probability he plays a rock song than a hip hop song will be:
= 15 / 40 - 11/40
= 15 - 11 / 40
= 4/40
= 1/10
= 0.1
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Adding phasers
Z1=2 / 63° Z2=5 / 42°
What’s is z1+z2
Answer:
the sum of Z1 and Z2 is 4.553 + j 5.326.
Step-by-step explanation:
To add two phasors, we add their real and imaginary parts separately.
Given:
Z1 = 2 / 63°
Z2 = 5 / 42°
Converting them to rectangular form:
Z1 = 2 cos(63°) + j 2 sin(63°) = 0.921 + j 1.862
Z2 = 5 cos(42°) + j 5 sin(42°) = 3.632 + j 3.464
Adding them:
Z1 + Z2 = (0.921 + 3.632) + j (1.862 + 3.464)
= 4.553 + j 5.326
Therefore, the sum of Z1 and Z2 is 4.553 + j 5.326.
hope this helped you!;))
A circular arc has measure 6cm and is intercepted by a central angle of 40°
Answer:
We can use the formula to find the length of a circular arc given the measure of the central angle and the radius:
Length of arc = (central angle measure / 360) x 2πr
where r is the radius of the circle.
Given that the central angle measure is 40° and the length of the arc is 6 cm, we can set up the equation:
6 = (40/360) x 2πr
Simplifying the fraction and solving for r, we get:
6 = (1/9) x 2πr
r = 9 x 6 / 2π
r = 27/π
So the radius of the circle is 8.59 cm (rounded to two decimal places).
Sue's class just held a class election. 21 students voted in the election and 4 did not. What percentage of the students voted ?
Answer:
84%
Step-by-step explanation:
The total is 25 students. (21+4)
The students that voted are 21
21/25 = 0.84
Graph each function and determine the y-intercept, then use the graph to determine the approximate value of the given expression. y = 9 Superscript x Baseline, 9 Superscript 0.8 a. 0; 2.6 c. 0; 4.9 b. 1; 3.4 d. 1; 5.8
The y- intercept for both function is 0 and 5.8.
We have First function
y= [tex]9^x[/tex]
Now , the y intercept of the equation is when x = 0
So , when x = 0
y= [tex]9^0[/tex]
y= 0
and, the second function is
y= [tex]9^{0.8[/tex]
y= 5.799
Hence, second function have intercept 5.8.
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Enter your answer in the box as a mixed number in simplest form.
A rectangular prism with the width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters.
cm³
The volume of the rectangular prism which is as described in the task content is; 67½ cm³.
What is the value of the rectangular prism?It follows from the task content that the value of the rectangular prism which is as described is required to be determined.
Since the rectangular prism has width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters;
Volume = l × w × h
Volume = 2½ × 6 × 4½
Volume = 5/2 × 6 × 9 / 2
Volume = 67½ cm³.
Ultimately, the volume of the prism is; 67.5 cm³.
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If the are of a triangle is 48ft2 and the hieght of the triangle is 12ft what would the length of the base be
Answer:
8 ft
Step-by-step explanation:
Area of a triangle=1/2*base*height
You know the area of the triangle and the height, so you can set up an expression to solve for the base
48=1/2*base*12
4=1/2*base
base=8ft
Check: A=1/2*8*12, A=48 ft²
К
1
A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates
a yearly profit of $1,275,000 if successful and a yearly loss of $425,000 otherwise. The probability of success is 1/2
If
the second mall is selected, it is estimated that the yearly profit will be $850,000 if successful; otherwise, the annual
loss will be $255,000. The probability of success at the second mall is
3
4
a. What is the expected profit for the first mall?
The expected profit for the first mall is $425,000.
How to calculate the expected profit for the first mallTo calculate the expected profit for the first mall, we need to multiply the profit for each outcome by its probability, and then add up the results.
Let S denote success and F denote failure for the first mall.
Then the expected profit is:
Expected profit for the first mall = (probability of success) × (profit for success) + (probability of failure) × (profit for failure)
Expected profit for the first mall = (1/2) × $1,275,000 + (1/2) × (-$425,000)
Expected profit for the first mall = $637,500 - $212,500
Expected profit for the first mall = $425,000
Therefore, the expected profit for the first mall is $425,000.
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The product of 4 and a number, all subtracted from 12.
The algebraic expression is represented as 12 - 4x
How to determine the expressionIt is important that we note that algebraic expressions are those expressions that are made up of some variables, certain terms, coefficients, factors and constants.
These algebraic expressions are also identified with the presence of arithmetic operations, such as;
Addition BracketParenthesesSubtractionMultiplicationDivisionFrom the information given,
Let the number by x
We then have;
The coefficient is 4
The constant is 12
The variable is x
Substitute the terms
12 - 4x
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Find the value of x.
78°
OA7
OB. 8
O C. 5
O D. 1
(12x+18)
Step-by-step explanation:
you can find the answer by vertical opposite angle
if the value of x is computed and it's equal to 78 you will find the answer
78=(12x+18)^
78=(12×5+18)
78=(60+18)
78=78 the problem is solved
may u get branliest please please
Need some help I’m stuck!!!!
Answer:
I think it’s
False
True
True
True
True
False
True
False
Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help Please help
Answer:
Step-by-step explanation:
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Which number should be added to the data so that the range of the data is 63?
78, 61, 95, 77, 85, 97
Answer:
124
Step-by-step explanation:
To find the number that should be added to the data so that the range of the data is 63, we first need to find the current range of the data.
The range of a set of data is the difference between the largest and smallest values in the set.
So, to find the current range of the data, we need to subtract the smallest value from the largest value:
Range = largest value - smallest value
Range = 97 - 61
Range = 36
This means that the current range of the data is 36.
To increase the range to 63, we need to add a number that is 63 - 36 = 27 larger than the current range.
To do this, we can add 27 to the largest value in the data set, which is 97:
97 + 27 = 124
So, we should add 27 to the data set to increase the range to 63.
Therefore, the complete set of data would be:
78, 61, 95, 77, 85, 97, 124
Check:
To find the range of the data set 78, 61, 95, 77, 85, 97, 124, we need to subtract the smallest value from the largest value:
Range = largest value - smallest value
Range = 124 - 61
Range = 63
Therefore, the range of the data set 78, 61, 95, 77, 85, 97, 124 is 63.
please find the area to question 4 on tuesday use link below
Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2
Step-by-step explanation:
What is the difference between the median math test score in the morning and the afternoon?
The difference between the median math test score, as shown by the ox plots, is: 12.5.
How to Find the Median in a Box Plot?The median of a data set is displayed in a box plot as the value that is at the vertical line that divides the rectangular box. This is also 50% mark of the data set.
Thus, the data set for afternoon, as shown in the box plot has a median that is 75, while the median of the data set for morning is 87.5.
Find the difference of their medians:
Difference of their medians = 87.5 - 75 = 12.5.
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Lab Assessment
1
2
3
b. -5
4
Active
What is the slope of the line that cuts through the points (1, -5) and (3, 5)?
a. 5
C.
1
d.
-
5
-1.5
Please select the best answer from the choices provided
The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the slope formula, we have the following;
Slope (m) = (5 - (-5))/(3 - 1)
Slope (m) = (5 + 5)/(2)
Slope (m) = 10/2
Slope (m) = 2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.
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