The formula to use for solving simple interest rate problems is:
[tex]i=\text{Prt}[/tex]Where
i is interest accumulated
P is the initial, or principal, amount
r is the rate of interest [in decimal]
t is the time
Given,
Total amount in account is 80 [principal plus interest]
rate is 2%
time is 8 years
Let's write:
[tex]\begin{gathered} 80=P+\text{Prt} \\ 80=P(1+rt) \\ 80=P(1+(0.02)(8)) \\ 80=P(1+0.16) \\ 80=P(1.16) \\ P=\frac{80}{1.16} \\ P=68.9655 \end{gathered}[/tex]The amount in the account was around $68.97
ate Fatuma Michele Simplify the expression below and identify the property used when eliminating the parentheses. 49 + 18 + 4 (29 + 9.5) 9+ The property was used to eliminate the parentheses. distributive commutative
Simplify the expression
[tex]\begin{gathered} 4q+18+4(2q+9.5)=4q+18+4\cdot2q+4\cdot9.5 \\ =4q+18+8q+38 \\ =12q+56 \end{gathered}[/tex]The distributive property is used to simplify the expression 4(2q + 9.5).
Answers:
12q + 56
Distributive property.
THE TOP OF A 20 FT. WATERSLIDEIS 16 FT. ABOVE THE GROUND.HOW FAR FROM THE BASE OF THESTEPS WILL THE GUESTS BE SHOTINTO THE WATER?
Using the given information, we form the following diagram.
To find x we use Pythagorean's Theorem.
[tex]20^2=16^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 400-256=x^2 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]Therefore, the answer is 12 feet.My I please get help with this math. I need help answering for each of them
State if the two triangles are congruent and by what thermoe
Although the triangles seems right triangles, we can't assume it because they might be out of scale.
So, the informations we have are:
They have a side wity equal length followed by a common side, thus it also has common length, and followed by an angle with common measure.
This is a case of Side-Side-Angle, and this is not enough to prove congruency.
So, the answer is that, we can't confirm if they are congruent or not.
You have a line AB where A is (0,3) and B is (2,7) find a point P that partitions the line 1:2.
ANSWER:
[tex]P=(\frac{2}{3},\frac{13}{3})[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula to calculate the point P
[tex]\begin{gathered} x_p=\frac{x_2\cdot a+x_1\cdot b}{a+b}_{} \\ y_p=\frac{y_2\cdot a+y_1\cdot b}{a+b}_{} \\ a\colon b=1\colon2 \\ (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,7) \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} x_p=\frac{2\cdot1+0\cdot2}{1+2}=\frac{2+0}{3}=\frac{2}{3} \\ y_p=\frac{7\cdot1+3\cdot2}{1+2}=\frac{7+6}{3}=\frac{13}{3} \\ \text{The point p is:} \\ (\frac{2}{3},\frac{13}{3}) \end{gathered}[/tex]I need help with this practice I believe the subject for this is complex numbers and vectors I will send you an additional picture that goes along with this, it is a graph, use the graph to answer
Solution
- In order to plot these vectors using Parallelogram law, we need to write them in rectangular form i.e. in terms of the x and y-components.
- This is done below:
[tex]\begin{gathered} \vec{a}=-3i-5j \\ \vec{b}=i+4j \end{gathered}[/tex]- We can then proceed to plot the vectors on a graph.
- For vector a, the line of magnitude extends from the origin (0, 0) to the point (-3, -5) while the line of the magnitude of vector b extends from the origin (0, 0) to the point (1, 4).
- This is shown below:
- The vector addition of both vectors is given below:
[tex]\begin{gathered} \vec{a}+\vec{b}=-3i-5j+(i+4j) \\ \text{ Add only magnitudes of the same component} \\ \vec{a}+\vec{b}=-3i+i-5j+4j \\ \\ \therefore\vec{a}+\vec{b}=-2i-j \end{gathered}[/tex]- This implies that the vector addition of both vectors extends from the origin (0,0) to the point (-2, -1)
- This is depicted below:
Reshanda bought 17 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 5 roses, and 6 daisies?
Given the word problem, we can deduce the following information:
1. Reshanda bought 17 plants to arrange along the border of her garden.
2. The plants are comprised of 6 tulips, 5 roses, and 6 daisies.
To determine the distinct arrangements that can she make, we use permutation as it an arrangement of objects in a definite order. The process is shown below:
[tex]Arrangements=\frac{n!}{p_1!p_2!p_3!}[/tex]where:
n=number of different objects=17
p1=objects of the first kind=6
p2=objects of the second kind=5
p3=objects of the third kind=6
We plug in what we know:
[tex]\begin{gathered} Arrangements=\frac{n!}{(p_{1})!(p_{2})!(p_{3})!} \\ =\frac{17!}{6!5!6!} \\ Calculate \\ Arrangements=5717712 \end{gathered}[/tex]Therefore, the answer is 5717712 arrangements.
Please help:A magazine publisher’s profit as a function of subscribers is represented in the table. The function is quadratic.Subscribers (thousands)Monthly profit ($ thousands)000.75−11.251.50220390Select from the drop-down menu to correctly complete the sentence.The x-intercept represents The images of the answer choice are included
In a profit function the x-intercept always represent the breakeven point, that is, the point where the amount of money to produce the product or service is equal to the amount of money received.
Hence, in this case, the x-intercepts represents the number of subscribers when the publisher breaks even.
Ricardo Cooks pizza at a restaurant he cooks five Pizza on Wednesday 9 pizzas on Thursday four times as many pizzas on Friday then Thursday complete the equation to show P the total number of Pizza is Ricardo Cooks on Wednesdays Thursdays and Fridays
this is the equation
total number of pizzas = pizzas cooked on Wednesday + pizzas cooked on
thursday + pizzas cooked on friday
total number of pizzas = 5 + 9 + 4(9)
total number of pizzas = 14 + 36
total number of pizzas = 50 This is the result
I have a calculus question about the definite integral, from my high school AP Calculus Class, pic included
Given the following definite integral.
[tex]\int_{-4}^4\sqrt{4^2-x^2}dx[/tex]We will use the substitution to solve the definite integral
Let the following:
[tex]\begin{gathered} 4sin(\theta)=x \\ 4cos(\theta)*d\theta=dx \\ And: \\ 4^2-x^2=4^2-4^2sin^2\theta=4^2(1-sin^2\theta)=4^2cos^2\theta \end{gathered}[/tex]Substitute into the given integral:
[tex]\begin{gathered} \int_{-4}^4\sqrt{4^2-x^2}dx=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sqrt{4^2cos^2\theta}*4cos(\theta)*d\theta \\ \\ =\int_{-\pi/2}^{\pi/2}4cos\theta *4cos\theta *d\theta=\int_{-\pi/2}^{\pi/2}16cos^2\theta *d\theta \end{gathered}[/tex]Now, we will use the following identity:
[tex]cos^2\theta=\frac{1}{2}(1+cos2\theta)[/tex]So, the integral will be:
[tex]\begin{gathered} =\int_{-\pi/2}^{\pi/2}\frac{16}{2}(1+cos2\theta)d\theta \\ \\ =8(\theta+\frac{1}{2}sin2\theta) \end{gathered}[/tex]substitute θ = π/2, and θ = -π/2
So, the value of the integral =
[tex]8*(\frac{\pi}{2}-(-\frac{\pi}{2}))=8π[/tex]So, the answer will be: Area = 8π
The graph of the given function is shown in the following picture
HELPPP!!
If Leo gets paid $125 in every paycheck and he immediately puts 50% into his savings account each time. How much money will he put into his savings accounts when he cashes the check?
Answer:
$62.5
Step-by-step explanation
125/2 can be simplified to 62.5/1 or just $62.5
An angle measures 24.6° more than the measure of its complementary angle. What is the measure of each angle? _and_
You have two angles, let's call them ∠1 and ∠2 of unknown measure, one of them measures 24.6º more than the other and both angles are complementary.
Let "xº" be the measure of ∠1, then ∠2 will beasure (x+24.6)º
∠1 and ∠2 are complementar, this means that together they add up to 90º
[tex]\angle1+\angle2=90º[/tex]Replace the expression with the angles measures
[tex]x+(x+24.6)=90[/tex]And solve for x
[tex]\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ \frac{2x}{2}=\frac{65.4}{2} \\ x=32.7 \end{gathered}[/tex]The angles measure:
∠1=32.7º
∠2=32.7+24.6=57.3º
what is 2/3 times 3/8
Mutiply both fractions:
[tex]\frac{2}{3}\times\frac{3}{8}[/tex][tex]\frac{2\times3}{3\times8}=\frac{6}{24}[/tex]Simplify by 6.
[tex]\frac{1}{4}[/tex]Answer:
Do the multiplication straight across 2 times 3= 6. 3times 8= 24 so 6/24 or 1/4
As part of a class project, a university student surveyed students in the cafeteria to look for a relationship between the students' eye color and hair color. The table contains the survey results. Match the descriptions with the correct values.
Ok, so
If we analyze the tab, we notice the following things:
- The number of students with blue eyes and blond hair is 42. That's because if we go to the table and look at the rows and columns, 42 is the number which relations these two facts.
- The number of students with gray eyes and brown hair, is 5. That's because if we go to the table and look at the rows and columns, 5 is the number which relations these two facts.
- The difference of the number of students with gray eyes and brown hair and the number of students with green eyes and black hair is:
- Green eyes and black hair - gray eyes and brown hair
=> 11 - 5, which is 6.
Select ALL the true statements1 poClare created Figure A Then she created Figure B by translating Triangle C and thentranslating Triangle D.Figure AFigureсDFigure A is congruent to Figure BFigure B is a translation of Figure A.Triangle Cis congruent to Triangle CTriangle D'is congruent to Triangle D.
The first statement cannot be true since the complete figure is not the same and sides cannot be overlapped together and look the same without a translation.
The second statement is not true either because if the full figure was translated it would look the same in another position and this is not the case.
The third and forth statements are true because figures were translated and didn't suffer any expansions or contractions which means that all of its sides must be equal and make them congruent.
Lindan just received a dozen roses for her birthday. For the flowers, she fills up a rectangular vase with water. The vase has a square bottom that is 3 inches in width. The base stands 12 inches tall. There is a sponge filling the bottom of the vase for the flower stands. It is 4 inches tall. How much space is left in the vase with for flowers?
Volume of the vase = 3 x 3 x 12 = 108 in^2
Volume of the sponge = 3 x 3 x 4 = 36 in^2
Volume left = 108 - 36 = 72 in^2
If f(x) = 2x^2 - 5 and g(x) = 2x + 1, evaluate f(g(x)) when x = -3
when x = -3
[tex]\begin{gathered} \Rightarrow[2(2\times-3+1)^2]-5 \\ 2[-5]^2-5=45 \end{gathered}[/tex]The final answer is 45
7+8=15 how do you decompose 10?I'm doing this for my granddaughter she's in the first grade and the teacher wants to know her dude examples 7 + 8 equals 15 and they want her to decompose it to make 10 then and use the number bond to show how you took two
To decompose 10 on basis of 8 it becomes 10 -2 =8
so 8 + 2 =10
Find the equation (in terms of x) of the line through the points (-4,-4) and (3,1)y=
In order to find the equation of the line, first let's calculate its slope m using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the given points (x1, y1) = (-4, -4) and (x2, y2) = (3, 1), we have:
[tex]m=\frac{1-(-4)}{3-(-4)}=\frac{1+4}{3+4}=\frac{5}{7}[/tex]Now, to find the equation, let's use the slope-intercept form and calculate the value of b using a given point:
[tex]\begin{gathered} y=mx+b \\ (3,1): \\ 1=\frac{5}{7}\cdot3+b \\ 1=\frac{15}{7}+b \\ b=1-\frac{15}{7} \\ b=-\frac{8}{7} \end{gathered}[/tex]Therefore the equation is y = (5/7)x - 8/7
What is the slope of the line in the graph?A. 8B. 1/8C. 1/4 D. 4
The slope of a line graph can be found using the formula:
[tex]\begin{gathered} slope\text{ = }\frac{y_2-\text{ y}_1}{x_2-x_1} \\ Where\text{ \lparen x}_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are two points on the line} \end{gathered}[/tex]From the graph, we have the points (0,0) and (8, 2)
Substituting the values into the formula:
[tex]\begin{gathered} slope\text{ = }\frac{2-0}{8-0} \\ =\text{ }\frac{2}{8} \\ =\text{ }\frac{1}{4} \end{gathered}[/tex]Answer:
slope = 1/4 (Option C)
1 of 9Place and label the following numbers on the number line.175-1.75Line Reader help me .
Ok, so:
We're going to place and label the following numbers on the number line.
-1
1.75
-1.75
-2
-2 1/2 = -3/2
-5/2
9/4
can you show me step by step how to divide 6 1/8 divided by 1 3/4
From the question we are asked to divide 6 1/8 by 1 3/4
To do this, we first convert this improper fraction to proper fraction
6 1/8 = 49/8
1 3/4 = 7/4
The next step is to convert to decimal.
49/8 = 6.125
7/4 = 1.75
So lets divide 6.125 by 1.75
6.125/1.75 = 3.5
Now let's convert the decimal back to fraction
3.5 in fraction = 7/2 = 3 1/2
So, 6 1/8 divide by 1 3/4 = 3 1/2
Which of the following shows that f(x) grows at the same rate as g(x)? (5 points)the limit as x goes to infinity of the quotient of f of x and g of x equals 1000the limit as x goes to infinity of the quotient of f of x and g of x equals 0the limit as x goes to infinity of the quotient of f of x and g of x equals infinityNone of these
The function f(x) grows at the same rate as the function g(x) according to the condition : [tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} =1000[/tex].
We are given two functions. The functions are f(x) and g(x). The definitions of the functions are not given explicitly, but we need to find the relationship between the functions. Both functions grow at a certain rate. We need to find the condition that shows that the function f(x) grows at the same rate as the function g(x). The ratio of the limiting values of the two functions must be a finite and non-zero constant for the functions to have the same rate of growth.
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MVT of a function x^2-6x+8 on (0,8)
According to the Mean Value Theorem:
[tex]f^{\prime}(c)\text{ = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex][tex]f^{\prime}(c)\text{ = }\frac{f(8)-f(0)}{8-0}[/tex]f(x) = x² - 6x + 8
f(0) = 0² - 6(0) + 8
f(0) = 8
f(8) = 8² - 6(8) + 8
f(8) = 64 - 48 + 8
f(8) = 24
f'(x) = 2x - 6
f'(c) = 2c - 6
[tex]\begin{gathered} 2c\text{ - 6 = }\frac{24-8}{8} \\ 2c\text{ - 6 = }\frac{16}{8} \\ 2c\text{ - 6 = 2} \\ 2c\text{ = 2 + 6} \\ 2c\text{ = 8} \\ c\text{ = }\frac{8}{2} \\ c\text{ = 4} \end{gathered}[/tex]compute the unit rate. round to the nearest hundredth. 226 Miles on 12 gallons
The unit rate of miles per gallon is computed dividing the number of miles and the number of gallons as follows:
[tex]\frac{226\text{ miles}}{12\text{ gallons}}=18.83\frac{\text{miles}}{\text{gallon}}[/tex]Which congruence theorems can be used to prove AEFG = AJHG? Select two options.
E
H
G
G
F
The options that can help prove that the triangles EFG and JHG are congruent are determined as follows:
Two triangles are said to be congruent (or the same) if:
i) One of the triangles has the lengths of all its sides equal to the lengths of the sides of the other triangle.
This scenario is called the SSS scenario
ii) One of the triangles has the lengths of two of its sides equal to the lengths of two sides of the other triangle, and then both of the two triangles have an angle in common.
This scenario is called the SAS scenario
From the above explanations, we can tell that the two triangles EFG and JHG will be congruent under the scenarios SAS and SSS
Thus options B and C are correct
A bottlenose dolphin is 10 feet belo sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation,y, after x seconds
Manuel has a bag of marbles with 2 blue marbles, 1 white marbles, and 1 red marbles.Find the following probabilities of Manuel drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.a) a blue, then a red b) a red, then white c) a blue, then a blue, then a blue
Explanation
We are given the following:
[tex]\begin{gathered} Bag=\begin{cases}{2\text{ }blue\text{ }marbles} \\ {1\text{ }white\text{ }marbles} \\ {1\text{ }red\text{ }marbles}\end{cases} \\ Total\text{ }marbles=2+1+1=4 \end{gathered}[/tex]We are required to determine the following probabilities:
[tex]\begin{gathered} (a)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }red \\ (b)\text{ }a\text{ }red,\text{ }then\text{ }white \\ (c)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue \end{gathered}[/tex]We know that probability is calculated as:
[tex]Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)}[/tex]For Question A:
We can determine the probability of a blue, then a red as:
[tex]\begin{gathered} P(blue\text{ }and\text{ }red)=P(Blue)\times P(Red) \\ =\frac{2}{4}\times\frac{1}{4}=\frac{2}{16}=\frac{1}{8} \\ \therefore P(blue\text{ }and\text{ }red)=\frac{1}{8} \end{gathered}[/tex]For Question B:
We can determine the probability of a red, then white as:
[tex]\begin{gathered} P(red\text{ a}nd\text{ w}h\imaginaryI te)=P(Red)\times P(Wh\imaginaryI te) \\ =\frac{1}{4}\times{}\frac{1}{4}=\frac{1}{16} \\ \operatorname{\therefore}P(red\text{ a}nd\text{ w}h\imaginaryI te)=\frac{1}{16} \end{gathered}[/tex]For Question C:
We can determine the probability of a blue, then blue, then blue as:
[tex]\begin{gathered} P(blue,blue,blue)=P(blue)\times P(blue)\times P(blue) \\ =\frac{2}{4}\times\frac{2}{4}\times\frac{2}{4}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \\ \therefore P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} (a)\text{ }P(blue\text{ }and\text{ }red)=\frac{1}{8} \\ \\ (b)\text{ }P(red\text{ a}nd\text{ w}h\mathrm{i}te)=\frac{1}{16} \\ \\ (c)\text{ }P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]2×9×5+32+4 Order of operation
2×9×5 + 32 + 4
First, we have to compute the multiplications
2×9×5 = 90
Then,
2×9×5 + 32 + 4 =
= 90 + 32 + 4
Now we only have additions, we can compute them
90 + 32 + 4 = 126
Which group of relatives make 25% of her guest she has 12 cousins 6 aunts 4 brothers 2 sister
From the statement of the problem, we know that the organizer has the following guests:
• 12 cousins,
,• 6 aunts,
,• 4 brothers,
,• 2 sisters.
The total number of guests is 12 + 6 + 4 + 2 = 24. A 25% of the total number of guests is 0.25*24 = 6 guests. Because the group of aunts has 6 members, that group represent 25% of her guest.
Answer
The group of 6 aunts represents 25% of her guests.