1. The decrease in dollars, based on a 7.5 percent decrease, is $615.
2. The balance in the account at the end of last year was $7,585.
What is a percentage?A percentage is a ratio or proportion of a variable in another.
For instance, the percentage decrease in the investment account was 7.5%, which in dollar terms amounts to $615.
The percentage reference gives an idea of the investment status and the fractional effect that the decrease had on it.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, Tammy's investment account decreased to $7,585 by $615, representing a 7.5% decrease.
Learn more about percentages at brainly.com/question/24877689
#SPJ1
20 POINTS, GET MARKED AS BRAINLIST IF RIGHT
P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.
What Are Independent Events?An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.
Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.
To determine P (B U C),
Given that B and C are independent.
Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675
To determine P (B U C),
Given that B and C are mutually exclusive.
Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.
Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.
Learn more about the Independent Events here:
https://brainly.in/question/4042290
#SPJ1
Given h(x) = –x – 3, find h(-6).
To find h(-6), replace x = -6 into the function, as follows:
h(x) = -x - 3
h(-6) = -(-6) - 3
h(-6) = 6 - 3
h(-6) = 3
The graph below shows Kate’s distance from her home(y), in miles, after a certain amount of time (x), in minutes:
The correct answer is Tim
She drives at a variable speed for 2minutes
The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven. Is the domain discrete or continuous?
Hello!
First, let me explain the difference between discrete and continuous.
Discrete: only some numbers of the interval are on the input. For example, in the interval 1 - 10, consider only the integers.
Continuous: all the numbers of the interval are on the input. For example: in the interval 1 - 10, all values are considered (integers and decimals).
Knowing it, let's analyze your exercise:
The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven.
We can represent miles as integers and also decimals, right?
• 2 miles
,• 5.750 miles
So, it means that all values can be considered.
Answer:So, this is a continuous domain.
11) At bank B, The value of us $700
is Bds $1.386. Calculate the
value of US $1.00 in BD $ at
this bank.
Answer:
Bds $ 1.98
Step-by-step explanation:
1386 bds / $ 700 * $ 1 = 1.98 Bds
He invested $ at 8% and Sat 12%
An actor invests some money at 8%, and $36000 more than twice the amount at 12%. The total annual interest earned
from the investment is $26400. How much did he invest at each amount? Use the six-step method.
K
oney at 8%, and $360
This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the
value of the variable x is 7.
let x = the money invested at 8%
y = the money invested at 12%
an actor invests some money at 8% and 36,000 more than four times the amount at 12%
x = 36000 + 2y
total annual interest earned from the investment is 26400
0.08*x + 0.12*y = 26400
by solving the system of equations
x = 36000 + 2y
0.08*x + 0.12*y = 26400
solving the equations,
0.08(36000+2y)+0.12y=26400
2880+0.16y+0.12y=26400
y=84000
x=204000
The amount for 8% will be 84000, and the amount for 12% will be 204000.
To know more about equations here,
https://brainly.com/question/14686792
#SPJ13
Hi, I was absent while my class learned this and I am unsure of how to solve for either. Any help/ explanation would be appreciated. Thanks!
Given: The figure shown
To Determine: The value of EF
Solution
Using intersecting chord theorem that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
Applying the theorem to the given would give us
[tex]CD\times DP=EF\times FP[/tex]Therefore
[tex]\begin{gathered} 11cm\times9cm=EF\times10cm \\ 99cm^2=EF\times10cm \\ EF=\frac{99cm^2}{10cm} \\ EF=9.9cm \end{gathered}[/tex]2. Let us label the the image given
PLEASEE HELP THIS IS DUE 2DAY!!!!!!
Create and solve a word problem using the equation 2×+12>2(×+6).include steps and strategies on how to solve the word problem
Can someone help me?? I just need 2 and 3
The current area of Mr. Milstein's kitchen table is:
[tex]=17\frac{1}{2}\text{ square fe}e\text{t}[/tex]The new width of Mr. Milstein's kitchen table = 5 feet
The area of the new kitchen table if the length is l is given by
[tex]\text{ Area (A) = length x width = 5l}[/tex]Note that the area of the proposed kitchen table should be larger than the current one.
[tex]\begin{gathered} \text{ The current area = }17\frac{1}{2}\text{ square fe}e\text{t} \\ \text{ The new area = 5 x l = 5l} \\ \text{ Therefore,} \\ \text{ proposed area > new area} \\ \text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t} \end{gathered}[/tex]Therefore,
[tex]\text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t can be used to get the length of the new table}[/tex]The correct option is F
what are possible dimensions of the rectangular area at the right
The expression used to depict area will be 9 / (3x - 1).
A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.
The given expression for area = 27x - 9
Factorize 27x - 9
Taking 9 as greatest common factor outside, we get
27x - 9 = 9(3x - 1)
We know that the area of rectangle with dimensions length by breadth is given by:-
Area = Length x Breadth
Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).
To know more about Dimensions
Refer this link:
brainly.com/question/27404871
#SPJ1
Complete Question:
What are possible dimensions of the rectangular area at the right? if area is 27x-9.
Patrick is a mountain climber. One morning, he drove to the base of a mountain whichwas at an elevation of 900 meters. While he climbed, he gained an average of 45 metersof elevation per hour. What is the slope and y-intercept of the function representingPatrick's elevation during his climb?
45 represents the slope while -900 is the y-intercept of the function
Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing
From the question, we are told that he averaged an elevation of 45 meters per hour
What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope
To get the y-intercept of the function, we can see this as a distance of -900 meters
The reason for this is that we can see the summit of the mountain as 0 m
So we can represent the equation as;
[tex]y\text{ = 45x-900}[/tex]Which of the following boxes should replace the question mark (?) to complete the pattern?
The most appropriate choice for pattern will be given by
Option E is the correct option
What is pattern?
Repeated arrangement of number or shape is called pattern.
Here,
Let the boxes be counted row wise
The question is all about filling all the blank boxes with orange colour.
Let the pattern be solved column wise
In the first column,
In first figure
The 2nd, 3rd and 4th boxes are filled with orange colour
Then in the second figure 5th box is filled with orange colour
To complete filling all the boxes with orange colour, 1st, 6th, 7th, 8th and 9th boxes are left. That is shown in the third figure.
In the third column
In first figure
The 5th, 6th and 9th boxes are filled with orange colour
Then in the second figure
1st, 2nd, 4th, 7th and 8th boxes are filled with orange colour
To complete filling all the boxes with orange colour, only the 3rd box is left
That is shown in third figure
Now, in the second column,
In the first figure,
1st, 7th and 8th boxes are filled with orange colour.
Then in the second figure 3rd, 6th and 9th are filled with orange colour
To complete filling all the boxes with orange colour, 2nd, 4th and 5th boxes are left.
That is shown in option E
So option E is correct
To learn more about pattern, refer to the link-
https://brainly.com/question/17386984
#SPJ9
Part 1 of 2
Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than $10,000. The price of car Ais $130,745
a. Assuming that you do not know which model is more expensive, write an absolute value inequality that describes this situation. Use x for the price of car B.
b. What are the possibilities for the price of car B?
The absolute value inequality is given by | x-130745 | > 10000
and the possibility of Car B is x < 120745 or x > 140745
What is absolute value inequality?
Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.
x = price of car B
x-130745 = difference in price from car A to car B
If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.
In short,
x-130745 > 0 when x > 130745
x-130745 < 0 when x < 130745
Using absolute value will give us
|x-130745| = positive difference in price
The result of an absolute value is never negative
We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar
| x-130645 | > 10000
Part b.
We'll use the idea that if |x| > k, then x < -k or x > k
to get the following
|x-130745| > 10000
x-130745 < -10000 or x-130745 > 10000
x < -10000+130745 or x > 10000+130745
x < 120745 or x > 140745
Car B has a price less than $120,745
OR
Car B has a price greater than $140,745
So basically anything that is not between 120745 and 140745. The price has to be positive of course.
To know more about absolute value inequalities, visit:
https://brainly.com/question/13344207
#SPJ9
Many graduate schools require applicants to take a certain test. Those taking the test receive three scores: a verbal reasoning score, a quantitative reasoning score, and an analyticalwriting score. In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points, and the average verbal reasoning score exceeded theanalytical writing score by 150.5 points. The sum of the three average scores was 305.9. What was the average score for each category?The average verbal reasoning score was (Type an integer or a decimal.)The average quantitative reasoning score was (Type an integer or a decimal.)The average analytical writing score was (Type an integer or a decimal.)
Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:
a verbal reasoning score,
a quantitative reasoning score,
an analytical writing score.
Let average verbal reasoning score represent by v
Let average quantitative reasoning score represent by q
Let average analytical writing score represent by a
In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points
i.e.,
Average quantitative reasoning score - average verbal reasoning = 1.3
q - v = 1.3 ...(1)
The average verbal reasoning score exceeded the analytical writing score by 150.5 points.
i.e.,
Average Reasoning score - average analytical writing = 150.5
v - a = 150.5 ...(2)
The sum of the three average scores was 305.9.
i.e.,
v + q + a = 305.9 ...(3)
Simplify the equation (1), (2) and (3) to get the value of q,v and a;
Add equation (1) and (2)
(q-v) + (v-a) = 1.3 + 150.5
q + a = 151.8 ....(4)
Substitute the value of (q+a=151.8) in the equation (3);
v + q + a = 305.9
v + 151.8 = 305.9
v = 305.9 - 151.8
v = 154.1
Substitute the value of v = 154.1 in the equation (2);
v - a = 150.5
154.1 -a = 150.5
a = 154.1 - 150.5
a = 3.6
Now, substitute the value of a = 3.6 in the equation (4)
q + a = 151.8
q + 3.6 = 151.8
q = 151.8 - 3.6
q = 148.2
Answer :
The average verbal reasoning score was 154.1
The average quantitative reasoning score was 148.2
The average analytical writing score was 3.6
What is the value of x in the equation -2 = 5x + 3?
A 1
B 1/5
C-1
D-3 2/5
Answer:
C
Step-by-step explanation:
- 2 = 5x + 3 ( subtract 3 from both sides )
- 5 = 5x ( divide both sides by 5 )
- 1 = x
how many integers are from 31 to 40
The number of integers from 31 to 40 is 10
What are integers?Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.
From the question, we are to determine the number of integers there are from 31 to 40.
First, we will list all the whole numbers from 31 to 40.
The whole numbers from 31 to 40 are
31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.
All of these numbers are positive whole numbers. Thus, they are integers.
The number of integers listed above is 10.
Learn more on Integers here: https://brainly.com/question/17225542
#SPJ1
tammy deposits $8,000 into an account that pays simple interest at a rate of 3% per year how much interest will she be paid in the first 4 years
Given this equation, what would the restriction be?X+6/x= -7
Given:
The equation is:
[tex]x+\frac{6}{x}=-7[/tex]Find-:
Restrictions for this equation
Explanation:
The equation is:
[tex]\begin{gathered} x+\frac{6}{x}=-7 \\ \\ \frac{x^2+6}{x}=-7 \end{gathered}[/tex]The denominator is not equal to zero. If the denominator is zero, then the function is undefined.
Then the restriction is:
[tex]x\ne0[/tex]For the function value of x is:
[tex]\begin{gathered} \frac{x^2+6}{x}=-7 \\ \\ x^2+6=-7x \\ \\ x^2+7x+6=0 \\ \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} x^2+6x+x+6=0 \\ \\ x(x+6)+1(x+6)=0 \\ \\ (x+6)(x+1)=0 \\ \\ x=-6\text{ and }x=-1 \end{gathered}[/tex]So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1
[tex][/tex]I need help with this question but no one is helping me! Can someone please help me
Answer:
Find the following probabilities if you are dealt cards from a standard 52-card deck. Round your answers to three decimal places.
a. If a card is randomly selected, what is the probability that the card is a heart?
13/52 = 1/4
b. If a card is randomly selected, what is the probability that the card is either a club or a spade?
26/52 = 1/2
c. If a cards is randomly selected, what is the probability that the card is both a club and a spade?
0
d. If two cards are randomly selected, what is the probability of drawing a three first, then drawing a jack?
4/52·4/51 = 4/663 = 0.006033182503
e. If two cards are randomly selected, what is the probability of drawing a heart first, then drawing a diamond?
13/52·13/51 = 13/204 = 0.06372549019
f. If two cards are randomly selected, what is the probability of drawing a face card followed by drawing an ace?
12/52·4/51 = 4/221 = 0.01809954751
g. If two cards are randomly selected, what is the probability of drawing a diamond first, then drawing an eight?
12/52·4/51 + 1/52·3/51 = 1/52 = 0.01923076923
On a public transportation map, two stations are 9 centimeters apart, whereas in real life thedistance between them is 3 kilometers. What is the scale of the map?Write your answer in simplest form using whole numbers.centimeters =kilometers
Given:
The distance between two stations in map, D= 9cm.
The distance between two stations in real life, d=3 km.
Now, to find the scale of the map take the ratio of D/d .
[tex]\frac{d}{D}=\frac{3\operatorname{km}}{9\text{ cm}}=\frac{1\operatorname{km}}{3\text{ cm}}=\frac{1}{3}\frac{km}{\operatorname{cm}}[/tex]So, the scale of the map is 1 km=3 cm.
A grandfather wants to know the average height of all his grandchildren. He finds that the heights of his 9 grandchildren aregiven in inches by
mean = sum of the heights / number of grandchildren
[tex]=\frac{63+71+60+59+74+60+60+75+58}{9}[/tex][tex]=\frac{580}{9}[/tex][tex]\approx64.4[/tex]A body is moving in simple harmonic motion with position function
s(t)= 4 + 5 cos t
Find the body’s velocity at t= 2π/3
The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)
How to find the velocity of a body under simple harmonic motion
Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:
y = y' + Δy · cos ωt (1)
Where:
y' - Initial positionΔy - Amplitudeω - Angular frequency.t - TimeThe equation for the velocity of the body in simple harmonic motion is found differentiating (1):
v = - ω · Δy · sin ωt (2)
If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:
v = - 1 · 5 · sin (2π / 3)
v = - 5 · sin (2π / 3)
v = - 5 · √3 / 2
v = - 5√3 / 2
The velocity is equal to - 5√3 / 2.
To learn more on simple harmonic motion: https://brainly.com/question/2195012
#SPJ1
An expression is shown below.
(3x² + 2x − 5) − (5x² − 4x + 1)
A)-2x² +6x-6
B)-2x² - 2x - 4
8x²+6x-6
D) 8x² - 2x - 4
Answer:
Result of [tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex] is [tex]\tt{} - {2x}^{2} + 6x - 6.[/tex]
Step-by-step explanation:
[tex] \tt{}(3 {x}^{2} + 2x - 5) - ( {5x}^{2} - 4x + 1)[/tex]
[tex]\tt{} {3x}^{2} + 2x - 5 - {5x}^{2} + 4x - 1[/tex]
[tex]\tt{} - {2x}^{2} + 6x - 6[/tex]
The midpoint M and one endpoint of CE are given. Find the coordinates of the other endpoint.
M(2,9) and C(4,12)
Hence, the coordinates of other point (x, y) are (0,6).
i.e. (x, y) → (0,6)
Let AB be the segment where
The coordinate M(2, 9) and C(4, 12)
and we have to find the point E.
Let us assume the other point is (x, y)
As we know that
The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.
Mid - point formula:
m = [tex]\frac{x_{1}+x_{2} }{2}[/tex]
n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]
So,
Substituting M(2, 9) into C(4, 12):
2 = [tex]\frac{4+x_{2} }{2}[/tex]
9 = [tex]\frac{12+y_{2} }{2}[/tex]
Solve the Equation:
[tex]x_{2} = 0\\y_{2} = 6[/tex]
Express solutions in ordered pairs:
(0,6)
Hence, the coordinates of other point (x, y) are (0,6).
i.e. (x, y) → (0,6)
Learn more about Midpoint at:
https://brainly.com/question/24463179
#SPJ1
What is the fewest number of points you must plot in order to have examples of all four sets of numbers, including at least one positive and one negative integer? Explain.
To which sets do positive integers belong? Select all that apply.
A.
Integers
B.
Natural numbers
C.
Whole numbers
D.
Rational numbers
1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.
2) The sets that positive integers belong to among the available are;
possibilities
Choices A, B, C, and D
1) There are two basic categories into which numbers are often divided:
- Rational numbers
- Irrational numbers
The four examples above are all different categories of rational numbers.
Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.
Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.
In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers
Learn more about Rational numbers Visit:
https://brainly.com/question/24398433
#SPJ1
A player kicks a soccer ball from a height of 2 feet. The ball reaches A maximum height of 20 feet after traveling 40 feet horizontally. And is caught by the goalkeeper 70 feet from where it was kicked. The path of the ball can be modeled by a parabola where why is the height in feet an exit the horizontal distance traveled in feet. At what height is the goalkeeper catch the ball?
The height is 9.875 feet from which the goalkeeper catches the ball.
The player kicks soccer from a height of 2 feet
x = 0 and y = 2
Maximum height of 20 feet after traveling 40 feet
x = 40, y = 20
So let y = a(x - 40)² + 20 ( the path of parabola)
Since x = 0 , y = 2
So, 2 = a(0 - 40)² + 20
2 = 1600a + 20
-18 = 1600a
a = - 9/800
Thus, y = -9/800(x - 40)² + 20
Since the soccer is caught by the goalkeeper 70 feet from where it was kicked
x = 70
So at this time,
y = -9/800 ( 70 - 40)² + 20
= -9/800 × 900 + 20
= - 81/8 + 20
= 79/ 8
= 9.875 feet
Therefore the height at which the goalkeeper catches the ball is 9.875 feet.
To know more about the height refer to the link given below:
https://brainly.com/question/27030273
#SPJ1
What is the solution to the division problem below? (You can use long divisionor synthetic division.)2x3 - 4x2 – 3x-9X-3A. 2x2 + 3x + 3B. 2x2 + x + 3C. 2x2 + 4x + 3O D. 2x2 + 2x+3
The answer for this process of long division is, therefore:
[tex]q=2x^2+2x+3[/tex]To find the result for this long division, we needed to divide the first term of the polynomial by the x in the divisor. Then, if we see the first graph, we have:
[tex]\frac{2x^3}{x}=2x^2[/tex]Then, we need to multiply this term by the divisor (x - 3), and then, subtract the result from the first two terms of the dividend. We can see as follows:
Already got b I just need a
[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.
Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
The quadratic equation with roots -7, 3/4 in standard form is
4x² + 25x - 21 = 0.
What is a quadratic equation?A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.
We know the roots of a quadratic equation are also factors of a quadratic equation.
If x = a and x = b are two roots of a quadratic equation then x - a = 0 and
x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.
Given that -7 and 3/4 are the roots.
∴ { x - (-7)}{ x - 3/4) = 0.
(x + 7)(x - 3/4) = 0.
x² + 7x -(3/4)x - 21/4 = 0.
x² + (25/4)x - 21/4 = 0.
4x² + 25x - 21 = 0.
learn more about quadratic equations here :
https://brainly.com/question/17177510
#SPJ1
4. Understand Draw two lines of reflection through point A so that the composition of the reflections across the lines maps onto the image shown.
When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.
Notice that the triangle get's inverted on each reflection around the lines.