General Idea:
The formula to find the Amount 'A' that need to be paid after ' t ' years for a Principal ' P ' with a annual rate of interest ' r ' is given below:
[tex] A= P(1+r \cdot t) [/tex]
Applying the concept:
Annie's cafe borrows $6100 at 6% for 290 days.
From the above statement we can conclude,...
[tex] P= \$6100\\ \\ r=6\%\\ \\ t=\frac{260}{365} [/tex]
Substituting the values of P, r and t in the formula, we get...
[tex] A=6100 \cdot (1+6 \% \cdot \frac{260}{365} )\\ \\ A=6100(1+\frac{6}{100} \cdot \frac{260}{365} )=6100(1+\frac{1560}{36500} ) \approx 6361 [/tex]
Conclusion:
The total amount that must be repaid after 290 days is approximately [tex] \$6361 [/tex]
which graph represent the equation y - 2 = 3x?
The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.
The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.
Volume of the globe=[tex] \frac{4}{3} \pi r^{3} [/tex]
Volume of the globe=[tex] \frac{4}{3}*3.14*7.5^{3} [/tex]
Volume=[tex] \frac{4}{3}*3.14*421.875 [/tex]
Volume=[tex] \frac{4}{3}*1324.6875 [/tex]
Volume=[tex] \frac{5928.75}{3} [/tex]
Volume=1766.25[tex] inches^{3} [/tex]
Volume of Globe=1766.25[tex] in^{3} [/tex]
Answer: 1766.25
Step-by-step explanation: tryust
What would be the radius of A= 907.46 square feet
Jatonia sold n cups of lemonade at her stand for $0.75 each. She made a total of $18.00. Write an expression to express how many cups of lemonade she sold.
What is the sum of the series?
An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 0.3 rad, b = 0.85 rad/s2 and c = 0.035 rad/s3
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
We have,
The equation θ(t) = a + bt² - ct³ represents the angular position of a point on the amusement park ride as a function of time.
Given:
a = 0.3 rad
b = 0.85 rad/s²
c = 0.035 rad/s³
In this equation,
θ(t) represents the angular position of the point on the ride at time t.
The term a is the initial angular position when t = 0, which is 0.3 radians.
The term bt² represents the angular displacement due to the linearly increasing angular velocity.
The coefficient b determines the rate of change of the angular displacement over time.
The term -ct³ represents the angular displacement due to the cubic decrease in angular acceleration.
To find the angular position at a specific time t, substitute the given values of a, b, c, and the desired value of t into the equation
θ(t) = a + bt² - ct³.
For example, if we want to find the angular position at t = 2 seconds:
θ(2) = 0.3 + 0.85 * (2²) - 0.035 * (2³)
= 0.3 + 0.85 * 4 - 0.035 * 8
= 0.3 + 3.4 - 0.28
= 3.42 radians
Therefore,
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
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The angular position of a point on a ride is given by the equation θ(t) = a + bt² - ct³. Factors such as the moment of inertia can change the angular acceleration in the system. When a child is on the merry-go-round, the moment of inertia increases, leading to a decrease in angular acceleration.
Explanation:The angular position of a point on an amusement park ride can be described by the equation θ(t) = a + bt² - ct³. In this equation, angular position is represented by θ(t), 'a' represents the initial angular position (0.3 rad), 'b' represents the angular velocity (increase in angular position per unit time - 0.85 rad/s2) and 'c' is the rate of change in angular velocity or the angular acceleration (0.035 rad/s3).
The angular acceleration can change due to factors such as a change in the moment of inertia. For example, when a child is on a merry-go-round, the combined moment of inertia is greater, therefore reducing the angular acceleration. The moment of inertia depends on factors such as the mass and the location of that mass relative to the axis of rotation. The child can be approximated as a point mass at a distance of 1.25 m from the axis of rotation.
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Jack is in hospital and his temperature is recorded every hour one morning. Time Temperature 06:00 40.0 07:00 40.0 08:00 39.5 09:00 39.0 10:00 38.5 11:00 38.0 12:00 38.0 Which is the best type of chart to use to represent this information? scatter diagram, pictogram, pie chart, line graph, tally chart, bar chart?
Here we are given two types of data : Time and Temperature.
We can plot one of these on x axis and the other on y axis.
So we can use a line graph here.
It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function?
Nt = 350,000(0.52)t
A 87,500
B 25,591
C 175,000
D 21,875
Answer: B
Step-by-step explanation:
plato
Sketch the asymptote and graph the function y=8/(x+3)-2
Answer:
Please find the attached file.
Step-by-step explanation:
Given: [tex]y=\dfrac{8}{x+3}-2[/tex]
We need to draw the graph of function with asymptote.
For horizontal asymptote:-
[tex]x\rightarrow \infty[/tex]
[tex]y=\lim_{x\rightarrow \infty}(\dfrac{8}{x+3}-2)=-2[/tex]
HA: y=-2
For vertical asymptote:-
[tex]y\rightarrow \infty[/tex]
[tex]x+3=0[/tex]
VA: x=-3
For x-intercept, Put y=0
(1,0)
For y-intercept, Put x=0
(0,2/3)
Now we will plot on graph and draw the graph.
Please see the attachment for graph.
Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x?
The solution to the mathematical inequality equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
Explanation:In order to find the solution to the equation 0.35x - 4.8 < 5.2 - 0.9x, you first need to rearrange the terms in the equation such that all terms involving x are on one side of the inequality and the other terms are on the other side. Starting with: 0.35x - 4.8 < 5.2 - 0.9x, if we add 0.9x to both sides we get 0.35x + 0.9x < 5.2 - 4.8, which simplifies to 1.25x < 10.
Next, to isolate 'x' we divide through by 1.25, which gives us: x < 10/1.25 which simplifies to x < 8. Therefore the answer to the equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
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define a variable and write each phrase as an algebraic expression
2 less than one-third of the points that the Panthers scored
Which of the following shows the graph of y = 4x + 3?
The graph of [tex]y=4x+3[/tex] is a line with a slope of 4, meaning for every unit moved to the right on the x-axis, you move up four units on the y-axis. The y-intercept is 3, so the line intersects the y-axis at the point (0,3). We plot these points and draw the line through them for the complete graph.
Explanation:The question asks, which of the following shows the graph of [tex]y = 4x + 3?[/tex]This is a linear equation in the format of y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. In this case, 'm' is 4, so for every step you move to the right on the x-axis, you move four steps up on the y-axis. 'b' is 3, so the line intersects the y-axis at the point (0,3). To graph this equation, start at the point (0,3) and for every 1 unit you move to the right, move up by 4 units. Repeat this process with other values of x to find corresponding values of y. Points are then plotted on the graph and a line is drawn through them showing the relationship between x and y.
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Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.
b. At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
c. Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Answer:
Part A) The quantities are [tex]30\ piece\ of\ sushi[/tex] and [tex]20\ bagels[/tex]
Part B) [tex]\$80[/tex]
Part C) The income effect is a loss of [tex]\$20[/tex]
Step-by-step explanation:
Part A)
Let
x-----> the number of piece of sushi
y----> the original number of bagels
we know that
[tex]2x=60[/tex] ------> [tex]x=30\ piece\ of\ sushi[/tex]
[tex]2y=40[/tex] ------> [tex]y=20\ bagels[/tex]
Part B) At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
Bagels
[tex]20(1)=\$20[/tex]
Sushi
[tex]30(2)=\$60[/tex] -----> is the same
The total cost is
[tex]\$20+\$60=\$80[/tex]
so
The same quantities would have cost [tex]\$80[/tex]
Part C) Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Find the difference
[tex]\$100-\$80=\$20[/tex]
therefore
The income effect is a loss of [tex]\$20[/tex]
Write a Multiplication expression that shows 10 sixths
Find the missing term of the following sequence. . . . –2, __, 456, . . .
The answer should be
228
What is the truth value for the following conditional statement? If the snow is white, then the grass is red.
Final answer:
The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.
Explanation:
The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.
Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.
In playing Monopoly, rolling doubles three times in a row sends you to jail. What is the probability of rolling three consecutive doubles? a. 0.167 b. 0.5 c. 0.00463 d. 18.0
Lucy's employer pays 70% of the total cost of her family's health insurance plan, while Lucy pays the rest. If the total cost of the plan will increase from $450 per month to $650 per month, how much more will Lucy have to pay each month?
Lucy will have to pay $60 more each month.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Lucy's employer pays 70% of the total cost of her family's health insurance plan, while Lucy pays the rest. Then Lucy will be only 30%.
If the total cost of the plan will increase from $450 per month to $650 per month.
At $450, Lucy pays 30% of $450 = 0.3 x 450 = $135
At $650, Lucy pays 30% of $650 = 0.3 x 650 = $195
Then Lucy has to pay each month more will be
⇒ $195 - $135
⇒ $60
Lucy will have to pay $60 more each month.
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What methods can be used to solve quadratic equations?
A British company is sending you measurements for a table to build in your factory. The table top must be 50 cm × 75 cm. Your machine calibrates in inches. Find the size of the table in inches. (1 cm = .39 in) A. 89 in × 114 in B. 11 in × 36 in C. 19.5 in × 29.25 in D. 128.2 in × 192.3 in
Answer: C. 19.5 in × 29.25 in
Step-by-step explanation: (50 x .39) x (75 x .39)
The line of best fit for a scatter plot is shown: A scatter plot and line of best fit are shown. Data points are located at 0 and 1, 2 and 1, 2 and 3, 4 and 3, 4 and 5, 6 and 3, 7 and 5, 9 and 4. A line of best fit passes through the y-axis at 1 and through the point 4 and 3. What is the equation of this line of best fit in slope-intercept form?
Answer:
y = (1/2)x +1
Step-by-step explanation:
Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values
y = (1/2)x +1
Answer:
y = (1/2)x +1
Step-by-step explanation:
Given the two points on the line are (0, 1) and (4, 3), the line's equation can be written using the two-point form:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (3-1)/(4-0)·(x -0) +1 . . . . use the given point values
y = (1/2)x +1
Step-by-step explanation:
Find the number, if 5/7 of it is 15
The number is 21.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = M
5/7 of M = 15
This can be written as,
(5/7)M = 15
M = 15 x 7/5
M = 3 x 7
M = 21
Thus,
The number is 21.
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1. James buys a video game for his Xbox for $49.99, a controller for $34.95, and a walk through manual for $19.99. The sales tax in his area is 8.25%. What will be the total cost of his purchase?
Carson buys three pencils at $0.35 each, a box of crayons for $2.86, four notebooks at $1.99 each, and two pens at $1.09 each. Estimate the amount he spent on school supplies.
Answer with Step-by-step explanation:
Carson buys three pencils at $0.35 each.
Cost of 1 pencil=$0.35
So, Cost of 3 pencils=$1.05 (0.35×3=1.05)
Buys a box of crayons for $2.86.
four notebooks at $1.99 each.
Cost of 1 notebook=$1.99
So, Cost of 4 notebooks=$7.96 (1.99×4=7.96)
and two pens at $1.09 each.
Cost of 1 pen=$1.09
So, Cost of 2 pens=$2.18 (1.09×2=2.18)
We have to estimate the amount he spent on school supplies.
Total Amount spent=$(1.05+2.86+7.96+2.18)
= $14.05
Hence, Total amount spent by Carson on school supplies is:
$14.05
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.4%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
what is the answer to this solve for h 12h=180
Write an equation for the parabola whose vertex is at (4, 9) and which passes through (5, 24).
Tom is going to build a fence around his garden which is a rectangle measuring 8 m by 20 m. He will first put in posts which will be 4 m apart. If the posts cost $5.50 each, what will be the total cost for all the posts?
plz help! 7th grade advanced math!!!!! A car travels 1 /6 of the distance between two cities in 3/ 5 of an hour. At this rate, what fraction of the distance between the two cities can the car travel in 1 hour?
Find all the second partial derivatives. w = u9 + v7
Answer:
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Step-by-step explanation:
We can have the second partial derivatives of w in relation to u, v and uv. So
[tex]w = u^{9} + v^{7}[/tex]
[tex]w_{u} = 9u^{8}[/tex]
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{v} = 7v^{6}[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Final answer:
The second partial derivatives of w = u^9 + v^7 are w_uu = 72u^7, w_uv = 0, and w_vv = 42v^5.
Explanation:
To find all the second partial derivatives of w = u^9 + v^7, we need to differentiate twice with respect to each variable. Let's start:
First, find the first partial derivatives:
wu = 9u^8 (differentiating with respect to u)
wv = 7v^6 (differentiating with respect to v)
Now, take the second partial derivatives:
wuu = 72u^7 (differentiating wu with respect to u)
wuv = 0 (differentiating wu with respect to v)
wvv = 42v^5 (differentiating wv with respect to v)
So, the second partial derivatives of w = u^9 + v^7 are wuu = 72u^7, wuv = 0, and wvv = 42v^5.