Answers
The answers to both questions are as:
(a) the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35,
b) the amount of the final payment is $688.32.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
(a) For 5 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 5
[tex]A = 9900(1 + 0.08/2)^{(2*5)}[/tex]
A = $14,917.95
(b) For 10 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 10
[tex]A = 9900(1 + 0.08/2)^{(2*10)}[/tex]
A = $23,673.58
(c) For 15 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 15
[tex]A = 9900(1 + 0.08/2)^{(2*15)}[/tex]
A = $37,337.35
Therefore, the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35, assuming the interest is compounded semiannually.
To calculate the final payment, we can first find the balance of the loan at the end of the fifth year, and then use this as the principal to calculate the balance at the end of the tenth year.
The interest rate is 5% per year, compounded quarterly. This means that the quarterly interest rate is:
r = 5% / 4 = 0.0125
Let B be the balance of the loan after 5 years. Then we have:
B = 1000*(1 + r)²⁰- 200*(1 + r)⁴
where the first term is the future value of the initial loan after 5 years, and the second term is the present value of the first payment of $200.
Plugging in the values, we get:
B = 1000*(1 + 0.0125)²⁰ - 200*(1 + 0.0125)⁴
B = 1000*(1.0125)²⁰ - 200*(1.0125)⁴
B = 1346.49
So the balance of the loan after 5 years is $1346.49. We can use this as the principal to calculate the balance at the end of the tenth year, which is the final payment we are looking for.
Let P be the final payment. Then we have:
P = 1346.49*(1 + r)⁴⁰ - 800*(1 + r)²⁰
where the first term is the future value of the balance after 10 years, and the second term is the present value of the second payment of $800.
Plugging in the values, we get:
P = 1346.49*(1 + 0.0125)⁴⁰ - 800*(1 + 0.0125)²⁰
P = 1346.49*(1.0125)⁴⁰ - 800*(1.0125)²⁰
P = 688.32
So the amount of the final payment is $688.32.
hence, the answers to both questions are as:
(a) the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35,
b) the amount of the final payment is $688.32.
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Related Questions
Use the distributive property to solve 4 2/5 x 10. Where 4 2/5 is a fraction. Please show work so I can explain. Thank you.
Answers
Answer:
Step-by-step explanation:it will be 44/1 = 44
Since 4 2/5 x 10
We will use 10 as 10/1
and 4 2/5 as 22/5 so
22/5 x 10/1 we cross out the 5 and 10 since there a factor of each other
then it will be 22/1 x 2/1 it will be much easier
Then 22 x 2 = 44
1x1 = 1
=44/1 = 44
add me
1111111111111111111111111111111
Answers
The value οf the variable y is 9 when k is -3 in the given question.
What is variable?In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.
A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.
A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.
Given: y=k x
where, x= -3 and k= -3
we can find the value of y by multiplying k with x,
so, y=k x
now, putting values as follows:
we get, y = -3 × -3
= 9
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I need to find f(g) f(x) please
Answers
The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other.
What is inverse?The inverse of a function is a second function that "undoes" the effect of the first function. More specifically, if f is a function that maps elements from a set A to a set B, then its inverse function, denoted as f^(-1), maps elements from B back to A.
According to question:(a) To find f(g(x)), we need to substitute the expression for g(x) into f(x):
f(g(x)) = g(x) / (6 + g(x))
Substituting the expression for g(x) yields:
f(g(x)) = (6x / (1 - x)) / (6 + (6x / (1 - x)))
This equation can be made simpler by first locating a common denominator:
f(g(x)) = (6x / (1 - x)) / ((6(1 - x) / (1 - x)) + (6x / (1 - x)))
f(g(x)) = (6x / (1 - x)) / ((6 - 6x + 6x) / (1 - x))
f(g(x)) = (6x / (1 - x)) / (6 / (1 - x))
f(g(x)) = 6x / 6
f(g(x)) = x
To find g(f(x)), we need to substitute the expression for f(x) into g(x):
g(f(x)) = 6f(x) / (1 - f(x))
Substituting the expression for f(x) yields:
g(f(x)) = 6(x / (6 + x)) / (1 - (x / (6 + x)))
To simplify this expression, we can first find a common denominator:
g(f(x)) = 6(x / (6 + x)) / (((6 + x) / (6 + x)) - (x / (6 + x)))
g(f(x)) = 6(x / (6 + x)) / ((6 + x - x) / (6 + x))
g(f(x)) = 6(x / (6 + x)) / (6 / (6 + x))
g(f(x)) = x
(b) The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other. This means that when we apply one function and then the other, we get back to the original input value. Specifically, if we apply f(x) to x and then apply g(x) to the result, we get x back, and if we apply g(x) to x and then apply f(x) to the result, we also get x back. This is a useful property when analyzing functions and their relationships.
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Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
Answers
Substitute h(t) = 0 in the given equation:
-16t^2 + 32t + 48 = 0
Dividing both sides by -16:
t^2 - 2t - 3 = 0
Factorizing the equation:
(t - 3)(t + 1) = 0
So, the solutions are t = 3 or t = -1.
Since time can't be negative, the only solution that makes sense in this context is t = 3.
Therefore, the ball will hit the ground after 3 seconds.
11). Evaluate the definite integral.
Answers
The value of the definite integral is determined as -1/28.
What is a definite integral?A definite integral is a mathematical concept that represents the area under a curve between two specific points, called the limits of integration. The definite integral is denoted by the symbol ∫, and the limits of integration are written as a and b, where a is the lower limit and b is the upper limit.
To evaluate the definite integral, we will use the following method:
[tex]\int\limits^2_0 {- \frac{6x}{(3x + 2)^2} } \, dx ; u = 3x^2 + 2[/tex]
We can start by substituting [tex]$u=3x^2+2$[/tex], which gives us [tex]$du/dx=6x$[/tex], or [tex]$x,dx=du/6$[/tex].
Using this substitution, we can rewrite the integral as:
[tex]\int\limits^2_0 - \frac{6x}{(3x^2 + 2)^2} , dx &\\\\\\\=\ \int\limits^{u(2)}{u(0)} -\frac{1}{u^2},du/6\\\\\\&= \left[ \frac{1}{6u} \right]^{u(2)}{u(0)} \\\\\\&= \frac{1}{6}\left(\frac{1}{u(2)} - \frac{1}{u(0)}\right)\\\\\\\&= \frac{1}{6}\left(\frac{1}{3(2)^2 + 2} - \frac{1}{3(0)^2 + 2}\right) \\\\\\\&= \frac{1}{6}\left(\frac{1}{14} - \frac{1}{2}\right)\\\\\\\ &= \frac{1}{6}\left(-\frac{6}{28}\right) \\\\\\\\&= \boxed{-\frac{1}{28}}\end{align*}[/tex]
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A primary credit card holder has a current APR of 14.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent? 12.29% 14.75% 0.01% 1.23%
Answers
Answer:
12.29 I thin
Step-by-step explanation:
The monthly periodic interest rate is 0.01%.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
APR=14.75%
Now,
The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:
r = (1 + i/m)^(m/n) - 1
Where:
r = periodic interest rate
i = nominal annual rate
m = number of compounding periods per year
n = number of payments per year
In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:
r = (1 + 0.1475/12)^(12/12) - 1
r = (1 + 0.012292) - 1
r = 0.012292 or 1.23%
Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.
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Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
Answers
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
Answers
Initially, 1/4 of the tank was filled.
After adding 12 gallons, it was 3/4 full.
Increase in fuel filled portion =
[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]
So 2/4 of the tank = 12 gallons
1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons
4/4 of tank [tex]= 6\times4 = 24[/tex] gallons
____________________
Portion remaining to be filled =
[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]
Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons
So you need 6 more gallons to fill the tank
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answers
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
The height of an object launched into the air can be modeled by the graph shown.
When does the object return to the ground?
Answers
Answer:
9 seconds
Step-by-step explanation:
right side of the graph touches the x axis at 9
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answers
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
I will mark you brainiest!
If AB = 35,BC = 15, and EF = 60, then the value of DE IS
A) 140
B) 180
C) 200
D) 210
Answers
AB/BC = DE/EF
35/15 = DE/60
DE = 35*60 / 15
DE = 140
answer
A 140
A business analyst wants to determine if the prices of goods at a supermarket have changed significantly since the new owner of the company took over. She looks at the prices of ten items before the new owner took over compared to after the new owner started.
(Chart in photo below)
Based on the data in the table and using a significance level of 0.05, what is the correct P-value and conclusion?
A. With a t statistic of 1.4789 and a P-value of 0.173292, reject the no hypothesis that prices have not changed
B. With a T statistic of 1.4789 and a P value of 0.173292, fail to reject the null hypothesis. The prices have not changed.
C. With a T statistic of 0.7394 and a P value of 0.478505, reject the no hypothesis that prices have not changed.
D. With a T statistic of 0.7394 anda P value of 0.478505, fail to reject the no hypothesis that prices have not changed.
Please answer quickly, 100 points thank you !
Answers
Answer: Option A
Step-by-step explanation:
The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:
t = -1.4789
P-value = 0.173292
Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.
With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.
Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.
To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.
Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.
To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:
Mean difference = (0.30 - 0.07) / 10 = 0.023
Standard deviation = 2.967
t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394
The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.
Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:
Thus, the correct option is D.
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What are the steps to solving the following problem,
5x+4=19
List at least 4 steps
Answers
Answer:
5x+4=19
5x=19-4
5x=15
5x÷5=15÷5
x=3
5x=19-4
5x=15 /:5
X=3
Construct the confidence interval for the population variance for the given values. Round your answers to one decimal place.
n=9
, s2=17.3
, and c=0.98
Answers
With 98% confidence, we can say that the population variance is between 7.36 and 71.09.
What is probability?
Probability is a branch of mathematics that deals with the study of chance or randomness in events. It is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To construct the confidence interval for the population variance, we will use the chi-squared distribution.
First, we need to calculate the chi-squared values for the lower and upper bounds of the confidence interval using the following formulas:
χ²_L = (n - 1) * s² / χ²(α/2, n-1)
χ²_U = (n - 1) * s² / χ²(1-α/2, n-1)
where n is the sample size, s² is the sample variance, α is the level of significance, and χ²(α/2, n-1) and χ²(1-α/2, n-1) are the chi-squared values with α/2 and 1-α/2 degrees of freedom, respectively.
Substituting the given values, we get:
χ²_L = (9 - 1) * 17.3 / χ²(0.01, 8) ≈ 3.355
χ²_U = (9 - 1) * 17.3 / χ²(0.99, 8) ≈ 29.587
Next, we can use these chi-squared values to construct the confidence interval for the population variance:
(V_L, V_U) = [(n - 1) * s² / χ²_U, (n - 1) * s² / χ²_L]
Substituting the given values, we get:
(V_L, V_U) = [(9 - 1) * 17.3 / 29.587, (9 - 1) * 17.3 / 3.355]
Simplifying, we get:
(V_L, V_U) ≈ [7.36, 71.09]
Therefore, with 98% confidence, we can say that the population variance is between 7.36 and 71.09.
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ABCD is a trapezium. P is a point along AC such that AP=4PC. DC=1/4AB.
a) express PB in terms of a and b in its simplest form
b) express DP in terms of a and b in its simplest form
c) does DPB form a straight line?
Answers
Answer:
a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:
PC = CP = x - b
AP = 4(x - b)
Also, using the fact that DC = (1/4)AB, we have:
AD = x
AB = 4DC = x/4
BC = AB - AD = x/4 - x = -3x/4
Now, consider the similar triangles PBC and ABD:
PB/AB = BC/AD
PB/(x/4) = (-3x/4)/x
PB = -3/4(x/4) = -3x/16
Finally, substituting x = a + b, we have:
PB = -3(a + b)/16
b) Using the same similar triangles as in part (a), we have:
DP/DC = PB/BC
DP/(1/4)AB = PB/(-3x/4)
DP = -3/4(PB)(DC/BC)AB
DP = -3/4(PB)(1/4)/(AB - AD)AB
Substituting the expressions for PB, AB, and AD from part (a), we get:
DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4
DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)
DP = -3/16
So, DP = -3/16(a + b)
c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:
Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16
Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4
Since the slopes are not equal, DPB does not form a straight line.
circumference is 1884, what is the diameter
Answers
Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)
you get this from dividing 1884 by 3.14159 (pi)
All I need to know is the answer to this problem so I can compare mine.
Answers
Answer:
we will do TanA = perpendicular / Base
A = 35°
Tan 35° = 217 / W
value of Tan 35° is approx = 0.7
0.7 = 217/ W
W = 217 / 0.7
W = 310
Please help i need it!!!
Which has more kinetic energy, a 5 kg rock hitting a car at 25 m/s or a 10 kg rock hitting a car at 15 m/s? Use the formula kinetic energy = (½)mv². Show your work using the graphical equation tool (Σ button in the toolbar above the text box).
Answers
Answer:
Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car
Step-by-step explanation:
We can use the formula for kinetic energy, which is:
Kinetic energy = (1/2) x mass x velocity^2
Let's start by calculating the kinetic energy of the 5 kg rock hitting the car at 25 m/s:
Kinetic energy = (1/2) x 5 kg x (25 m/s)^2
Kinetic energy = 1562.5 J
Now let's calculate the kinetic energy of the 10 kg rock hitting the car at 15 m/s:
Kinetic energy = (1/2) x 10 kg x (15 m/s)^2
Kinetic energy = 1125 J
Therefore, the 5 kg rock hitting the car at 25 m/s has more kinetic energy than the 10 kg rock hitting the car at 15 m/s.
We can represent this visually using the following equations:
Kinetic energy of 5 kg rock hitting car = (1/2) x 5 kg x (25 m/s)^2 = 1562.5 J
Kinetic energy of 10 kg rock hitting car = (1/2) x 10 kg x (15 m/s)^2 = 1125 J
Σ Kinetic energy of 5 kg rock hitting car > Σ Kinetic energy of 10 kg rock hitting car
ASAP !
[tex]2 \frac{3}{6} - \frac{1}{3} [/tex]
Answers
The mathematical expression to be evaluated is:
[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]
To simplify the expression, we first convert the mixed fraction to an improper fraction:
[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]
Substituting this value back into the original expression, we get:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]
Now we need to find a common denominator for the two fractions:
[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]
We can simplify the second fraction:
[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
[tex]\frac{26}{12} = \frac{13}{6}[/tex]
Therefore, the simplified value of the mathematical expression is:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]
Answer:
[tex]2\frac{1}{6}[/tex]
Step-by-step explanation:
First, write the fractions as improper fractions.
[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]
To, subtract the fractions make the denominators the same.
For that, multiply both sides of 1/3 by 2.
[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]
Subtract.
[tex]\frac{13}{6}[/tex]
Write it as a mixed number.
[tex]2\frac{1}{6}[/tex]
Ronald likes to skate at a game store that is due south of his school and due west of his favorite skate park. If the game store is 7 miles from his school and the straight line distance between yhe school and the skate park is 8 miles, how far is the game store from the skate park?
Answers
Answer:
15 miles
Step-by-step explanation:
7 miles from game store to school plus another 8 miles from school to skate park equal 15.
A person travels 30 miles in 40 minutes
Answers
The distance that the person will be able to cover in an hour would be = 45 miles
How to calculate the distance travelled?The distance that the individual covers in in 40 mins = 30 miles.
Therefore in an hour(60 mins) the distance would be = X mile
That is ;
40 mins = 30 miles
60 mins = X
make X the subject of formula;
X = 60×30/40
X = 1800/40
x = 45 miles.
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Find an equation of the line that passes through the pair of points (4,5) & (-1, -1). Write the equation in the form Ax+By=C
Answers
In response to the stated question, we may state that Hence the slope equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
what is slope?Slope is just the curvature of a bend or line in mathematics. It is a measure of the manner in which the y-value of something like a function varies because when x-value changes. The slope of a line is commonly symbolized by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 options on the line. A bridge's slope might be negative, negative, zero, or unknown. A positive slope indicates that the line ascends to left to right, whereas a slope indicates that the line drops from left to right.
We must use the point-slope form of the equation of a line to obtain the equation of a line of the form Ax+By=C that goes through two points:
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is the location of one of the points and m is the line's slope.
Then, we must determine the slope of the line.
[tex]m = (y2 - y1) / (x2 - x1) (x2 - x1)\\where (4, 5) = (x1, y1) and (x2, y2) = (-1, -1)m = (-1 - 5) / (-1 - 4) = -6 / (-5) = 6/5\\y - y1 = m(x - x1) (x - x1)\\y - 5 = (6/5)(x - 4) (x - 4)\\5y - 25 = 6x - 24\\6x - 5y = -1\\[/tex]
Hence the equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
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Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answers
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
i’ll give brainlist
Answers
In response to the stated question, we may state that As a result, we can triangle only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
What precisely is a triangle?A triangle is a closed, two-dimensional geometric shape made up of three line segments called sides that intersect at three points called vertices. Triangles may be identified by their sides and angles. Based on their sides, triangles might be equilateral (all sides equal), isosceles, or scalene. Triangles are classed as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles more than 90 degrees) (all angles greater than 90 degrees). The area of a triangle may be calculated using the formula A = (1/2)bh, where A is the area, b is the base of the triangle, and h is the height of the triangle.
To demonstrate the similarity of two triangles, we must demonstrate that their respective angles are congruent and their corresponding sides are proportionate.
∆ABC ~ ∆PQR
We can see from the triangles that angle A is congruent with angle P, angle B is congruent with angle Q, and angle C is congruent with angle R. As a result, we have the angle-angle (AA) similarity:
∆ABC ~ ∆PQR
[tex]AC/PR = 13/16 \\AB/PQ = 5/8 \\BC/QR = 12/16 = 3/4 \\AC/PR = 13/16[/tex]
Because the matching side length ratios are not entirely equal, the triangles are not comparable according to the side-angle-side (SAS) similarity theorem. As a result, we can only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
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Number 5 Please look at image
Answers
The solutions to the quadratic equations are as follows
4a. The rocket was launched from an initial height of 10 meters.
b. The maximum height of the rocket was 55 meters.
c. The rocket reaches its maximum height at 3 seconds
d. the rocket is in the air for t = 6.316 seconds
5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet
b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.
How do we solve the quadratic equation?The function is a quadratic equation, and here is how we solve each problem;
a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:
h = -5(0)² + 30(0) + 10 = 10 meters
b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:
t = -b/2a = -30 / (2×-5) = 3 seconds
So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:
h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters
The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:
0 = -5t² + 30t + 10
This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)
Let's calculate the roots:
t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)
= [-30 ± √(900 + 200)] / -10
= [-30 ± √(1100)] / -10
= 6.316 or -0.32
5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:
h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet
b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:
h = -1/8(33)² + 4(33) + 5
h = -1/8×1089 + 132 + 5
h = -136.125 + 132 + 5
h = 0.875 feet
when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.
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88.128 x 0.5 Multiplication question
Answers
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
Suppose you have two six-sided dice where each side is equally likely to land face up when rolled.
What is the probability that you will roll doubles?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
What is the probability that you will roll a sum of twelve?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
Answers
Answer:
12/12 and 1/12
Step-by-step explanation:
(-8)-(-2) porfa lo necesito
Answers
Answer:
-6
Step-by-step explanation:
A quadratic function passes through the points (-2,5) and (-8,5) and has a graph in the xy-plane that opens downward. Which of these could be the coordinates of the highest point of the graph?
O (5, 1)
O (5, 8)
O (5, 1)
O (5, 8)
Answers
The highest point of the quadratic equation that opens down can be (-5, 8)
Which of these could be the coordinates of the highest point of the graph?We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).
The highest point will be of the form (x, y).
Such that y is larger than 5, and the value of x is right between the two values above:
x = (-2 - 8)/2
x = -5
So the point is of the form (-5, y) where again y > 5.
From the given options the only of this form is (-5, 8)
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