The rule of the simple interest is
[tex]I=P\times R\times T[/tex]P is the initial amount
R is the rate in decimal
T is the time in years
Since Kim places $1250, then
P = 1250
Since the rate is 4.25%, then
[tex]R=\frac{4.25}{100}=0.0425[/tex]Since the time is 60 months, divide it by 12 to change it to years
[tex]\begin{gathered} T=\frac{60}{12} \\ T=5 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} I=1250\times0.0425\times5 \\ I=265.625 \end{gathered}[/tex]Round it to the nearest hundredth
I = $265.63
For trapezoid WXYZ shown below, points U and V are the midpoints of the legs. Use this information to find UV, the length of the mid segment.
Given:
[tex]\begin{gathered} WX=x+7 \\ ZY=6x+5 \\ UV=8x-3 \end{gathered}[/tex][tex]\begin{gathered} UV=\frac{1}{2}(WX+ZY) \\ 8x-3=\frac{1}{2}(x+7+6x+5) \\ 2(8x-3)=(7x+12) \\ 16x-6=7x+12 \\ 16x-7x=12+6 \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Length of the midsegment=8x-3} \\ =8(2)-3 \\ =16-3 \\ =13 \end{gathered}[/tex]13 is the final answer.
1. (5 points) The arc of a football thrown by Patrick Mahomes is modeled by the equation h=-16t2 + 36t + 6, where h = the height of the ball and t = the time in seconds. Will the ball reach a height of 24 feet?
In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.
Proceed as follow:
h = 16t² + 36t + 6
24 = 16t² + 36t + 6
16t² + 36t + 6 - 24 = 0
16t² + 36t - 18 = 0
use he quadratic formula, given by:
[tex]t=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]In this case, a = 16, b = 36 and c = -18
[tex]\begin{gathered} t=\frac{-36\pm\sqrt[]{(36)^{2}-4(16)(-18)}}{2(16)} \\ t=\frac{-36\pm49.47}{32} \\ t_1=-2.67 \\ t_2=\text{0}.42 \end{gathered}[/tex]negative times do not have physical meanning, then, the available solution is
t = 0.42
Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.
Which is the domain and range of the parabola with the equation… Thanks
Okay, here we have this:
Considering the provided equation of the parabola, we are going to find the requested domain and range, so we obtain the following:
Domain: Corresponds to all the values that x can take in the function. Given that in this case no value of x indeterminates the function, and that x can take any value, then its domain will be: (-∞, ∞).
Range: Corresponds to all the values that the dependent variable can take. In this case, since it is a parabola of the form ax^2+bx+c, and that a is less than or greater than 0, its range will be all values greater than or equal to its y-coordinate of the vertex, which for this case is (5, -15). So its range is: [-15, ∞).
Therefore finally we obtain that the correct answer is the fourth option.
-2(-3.4)what is the answer
6.8
1) Let's calculate this product by distributing the factor -2 multiplying the number within the parentheses.
-2(-3.4) Equal signs yield positive and remove the parentheses
6.8
2) So 6.8 is the answer for that product.
Function g is represented by the table.
-1
0
24
4
X
g(x)
1
0
2
-
10
3
-24
to
Which statement correctly compares the two functions?
OA. They have different x- and y-intercepts but the same end behavior as x approaches.
OB.
They have the same x- and y-intercepts.
C.
They have the same y-intercept and the same end behavior as x approaches".
D. They have the same x-intercept and the same end behavior as x approaches".
The functions have the same x-intercept and the same end behaviour as x approaches infinity.
We are given two functions, f(x) and g(x). A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
The function f(x) is represented in the graph. The function g(x) is represented by the data in the table. We have to find the correct comparison between the two functions.
The comparison is to be done on the basis of the lengths of the x-intercept and y-intercept and the end behaviour of both functions. From the given values, we conclude that the x-intercepts for both functions are the same, but the y-intercepts are different. The end behaviour of both functions becomes similar as x approaches infinity.
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UU UN INSUL OUUU Convert a fration: m=- 4444 21 x= -2 3 2 91 40 = IU m=-5 2 and 3 32°+x- Which two integers does V5 go between? 1 and 2 49 x=100 x=180 7 and 8 4 and
I'll get the slope of the arrow on the graph
P1 = (-1, 1)
P2 = (-4, 3)
slope = m = (3 - 1) / (-4 + 1)
m = 2/-3
slope = m = -2/3
An empty bucket is being filled at a constant rate. after 4 minutes, the depth of the water is 12 inches. the water continues to be filled at that same rate. what is the relationship between the time in minutes, x, and the depth of the water, y?
Every 4 minutes, the depth of the water increases 12 inches. Like let's say after another 4 minutes it'll be 24 inches. I may be wrong but I may be right.
Answer:
See below
Step-by-step explanation:
Every minute 'x' produces 12/4 = 3 inches of 'y' water depth
y = 3 x
Heyyy.......please i need help with this
√ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We know that ,
Trigonometric identities
sin²θ+cos²θ=1
so 1-cos²θ= sin²θ
sec²θ+tan²θ=1
1-sec²θ=tan²θ
So √ 1-cos²θ/1-sec²θ
√ 1-cos²θ/1-sec²θ=√sin²θ/tan²θ
The square root will get cancelled
=sinθ/tanθ
=sinθ/sinθ/cosθ (because tanθ=sinθ/cosθ)
=cosθ
Hence √ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
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On the number line above, if x is a number that lies between a and a + 10, which of the following must betrue?lx - al > 5lx - a -51 < 5lx - a - 101 < 5lx - a + 101 < 5
We are given an inequality proble. Our approach is to test our options.
We begin with the second option.
[tex]\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}[/tex]We'll solve it in parts and compare to our number line
[tex]\begin{gathered} -5<(x-a-5) \\ \text{Adding 5 to both sides gives us:} \\ -5+5On the other hand, we have:[tex]\begin{gathered} (x-a-5)<5 \\ \text{Adding 5 to both sides} \\ x-a<5+5 \\ x-a<10 \\ \text{Adding a to both sides} \\ x<10+a \end{gathered}[/tex]The range of x is therefore: a < x < 10 + a
SECOND OPTION
A normal distribution has a mean of 75 and a standard deviation of 15.
Determine the z-score for the data value of 85.
0.67
1) Given that we've got the following data:
[tex]\mu=75,\sigma=15,X=85[/tex]We can plug them all together into the Z score formula:
[tex]Z=\frac{X-\mu}{\sigma}=\frac{85-75}{15}=\frac{10}{15}\approx0.67[/tex]Thus, the Z-score is 0.67
A rectangular prism gift box has dimensions of 2.5 inches, 7 inches, and 9 inches.How much wrapping paper will it take to cover the gift box? Round answer to the nearest tenth if necessary.
The question requires us to calculate the surface area of the rectangular prism.
The formula to calculate the surface area is given to be:
[tex]A=2\left(wl+hl+hw\right)[/tex]where l is the length, w is the width, and h is the height.
From the question, the following dimensions are provided:
[tex]\begin{gathered} l=2.5 \\ w=7 \\ h=9 \end{gathered}[/tex]Therefore, we can calculate the surface area to be:
[tex]\begin{gathered} A=2(7\cdot2.5+9\cdot2.5+9\cdot7) \\ A=206\text{ in}^2 \end{gathered}[/tex]OPTION C is correct.
Which two consecutive integers does[tex] - \sqrt{214} [/tex]fall between?
Answer
-√214 is between -15 and -14.
Explanation
To solve this, we need to first obtain the value of the -√214
-√214 = -14.63
Hence, we can see that this number is between -15 and -14.
Hope this Helps!!!
What is the radian equivalent of 90 degrees?
Answer:
The Radiant Equivalent of 90 degrees, would be 1.57079633.
Which region has a population density less than 60 animals per square mile
Explanation
We will have to find the population density of each of the regions
To get the population density, we will have to divide the population of each region and then divide by the area of the of each region
For part A
[tex]Area=\frac{1}{2}\times40\times35=700mi^2[/tex]The population density of region A is
[tex]\frac{42500}{700}=60.71\text{ animals per square miles}[/tex]For region B
The area of region B is
[tex]\frac{1}{2}\times50\times38=950mi^2[/tex]The population density of region B is
[tex]\frac{60800}{950}=64\text{ animals per square miles}[/tex]For region C
[tex]area=\frac{1}{2}\times42\times49=1029mi^2[/tex]The population density of region C
[tex]\frac{57300}{1029}=55\text{ animals per square mile}[/tex]Thus, we can observe that Region C has a population density lower than 60 animals per square miles
Thus, option C is correct
what do you think the answer is? No it’s not the 3rd option or not that I think I just clicked a random answer on accident.
Answer
Option C is correct.
Sandra will be paid 72.30 dollars for babysitting for 12 hours.
Explanation
We are told that Sandra earned 60.25 dollars babysitting 10 hours.
If she babysits at the same rate, we are asked to calculate the amount she would earn if she babysits for 12 hours.
Let the amount Sandra is paid for babysitting for 12 hours be x dollars
10 hours = 60.25 dollars
12 hours = x dollars
We can write a mathematical relationship by cross multiplying
10 × x = 12 × 60.25
10x = 723
Divide both sides by 10
(10x/10) = (723/10)
x = 72.3 dollars
Hope this Helps!!!
Can someone please help me?
Part A) The definition of speed can be used to establish the equation of the line that depicts the relationship between distance and time, which is (y = 62x).
Part B) Option c
What is a speed, exactly?
Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path.
Given:
In 3 hours and 186 miles, Car X goes.
To find the equation of the line that represents the relationship between distance and time, perform the following steps:
Step 1: Assume that car X traveled a total distance of y miles and traveled that amount in x minutes.
Step 2: The speed is determined by the distance to time ratio.
speed = distance / time
Step 3: Add the distance and time values to the equation above.
Speed = y/x —— (1) (1)
Step 4 - Based on the provided information, the speed is determined by:
speed = 186/3 = 62
Step 5: Adding the speed value to the equation (1).
y/x = 62
y = 62x
(Y = 62x) is the equation of the line that depicts the relationship between space and time.
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A 6-pack of magnets costs $6.06. What is the unit price?
Answer: $1.01
Step-by-step explanation: You just divide by 6
Help with my algebra please.
t + b = 38
6t + 4b = 188 is the equation to calculate the system of the restaurant .
Restaurants must foster an atmosphere of delicious food, attractive surroundings, and courteous living. In order to maintain the restaurant's financial viability, it is crucial for the owners to choose the seating arrangement, chairs, and sofas with an eye toward projecting a certain image.
What is seat arrangement problems?The most typical categories of seating arrangement queries. There are intricate row arrangements, double rows, rectangular rows, linear rows, and circular rows.
Theatre. The simplest and most popular seating arrangement for events is the theater style setup.
Classroom.Herringbone.a U-shape.Equine shoeSquare HollowBoardroom.Banquet.n distinct things permuted (when repetition is not allowed) Repetition when it is acceptable. When the objects are not distinct, permutation (Permutation of multi sets)
The following formula determines how many permutations of n objects, taken r at a time: (n,r)! P(n,r)=n!
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.
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Write an equation of the line that passes through $\left(18,\ 2\right)$ and is parallel to the line $3y-x=-12$.
The equation of the line which is parallel to the given line is 3y - x = -12.
What is an equation?An equation is a mathematical formula containing an equal sign. Equations often involve algebra. Algebra is used in mathematics when we don't know the exact number in a calculation. In its simplest form in algebra, the definition of an equation is the mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. An equation is a mathematical expression consisting of two expressions connected by an equal sign. For example, 3x + 5 = -16 is an example of equation. Solving this equation gives the value of the variable x as x = 7.given that
x = 18 and y = 2
putting the value in equation 3y-x = -12
this saisfied he equation perfectly.
Hence, the equation in parallel to 3y-x = -12
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Please help now asap now !!!!!!!!!!!!
Answer: 771
Step-by-step explanation:
Reverse the equation for 96 x 8 + 3
96 x 8 = 768
768 + 3 = 771
You only add the 3 at the end since it was unable to be divided, you can't reverse and multiply it
what is 91 divided by 7 ??
Answer:
13
Step-by-step explanation:
[tex]\frac{91}{7}=\frac{70+21}{7}=10+3=13[/tex]
The solution of 91 divided by 7 in simplest form is,
⇒ 13
We have to given that,
To simplify 91 divided by 7 in simplest form.
It can be written as,
⇒ 91 ÷ (7)
⇒ 91 / 7
⇒ 13
Therefore, The solution of 91 divided by 7 in simplest form is,
⇒ 13
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Hey there Ms or Mr could you please help me out with this problem?just so you know, this is Pythagorean theorem & Simplifying Radicals My recent tutor said that this is the answer of course no I don't have any doubts I just want to know if this is correct.
When we have a radical, we can simplify it by the rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]So, we have to break down 500 into simpler radicals until we have a radical that can't be broken down. Let's simplify Root(500).
[tex]\sqrt[]{500}=\sqrt[]{50}\sqrt[]{10}[/tex]Now, we can break down Root(50) further.
[tex]\begin{gathered} \sqrt[]{50}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \end{gathered}[/tex]Now, let's break down Root(10) also, thus we have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \end{gathered}[/tex]We can see:
• Root(25) is 5
,• Also Root(2)*Root(2) is 2 by using the rule:
[tex]\sqrt[]{a}\sqrt[]{a}=a[/tex]Thus, we finally have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \\ =5(2)\sqrt[]{5} \\ =10\sqrt[]{5} \end{gathered}[/tex]The lines below are parallel. If the slope of the green line is -1/2,what is theslope of the red line?
When two lines are parallel they mean that both slopes are the same, this means that if the green line has a slope of -1/2, the slope of the red line is also -1/2.
Convert the polar equ what is the angle between the ropes? Round to the nearest degree.ation r = 16 sin θ to a rectangular equation.
The angle between the ropes is 53°.
We are given that a barge is being towed by two tugboats using ropes. The force vectors of the two tugboats are represented by F1 and F2. A vector is an entity that has both a magnitude and a direction. The vectors are F1 = 11000i + 5000j and F2 = 14500i + -8000j. We need to find the angle between the ropes. The best method is to find the dot product. Let the angle between the ropes be θ. We can say that cos(θ) = F1.F2/(|F1|*|F2|) = (11000*14500 + 5000*-8000)/[√[(11000)² + (5000)²] * √[(14500)² + (-8000)²]] = (11*14.5 + 5*-8)/[√[(11)² + (5)²] * √[(14.5)² + (-8)²]] = 119.5/[√146*√274.25] = 119.5/200.1 = 0.597. So, the value of θ is 53°.
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estimate the quotient .. 19 4/8 divided 4 5/8
about 3
about 6
about 5
about 4
The quotient 19 4/8 divided 4 5/8 is about 3
We need to estimate the quotient .. 19 4/8 divided 4 5/8
19 4/8 ÷ 4 5/8
Converting the mixed fraction 19 4/8 into improper fraction
(19x8 + 4)/8 = 154/ 8
Converting the mixed fraction 4 5/8 into improper fraction
(4x8 + 5)/ 8 = 45/8
Dividing 154/ 8 with 45 / 8
(154/8) / (45/8)
Multiplying both numerator and denominator with 8
154 / 45
3.2 = 3 (approx)
Therefore, the quotient .. 19 4/8 divided 4 5/8 is about 3
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Warm-up:
Determine the Cost of Goods Sold for one Holiday Basket:
1 basket $24.00 per dozen
2 lbs. Cheddar cheese $1.50 per pound
1 canned ham $60.00 per dozen
3 jars of jelly $1.00 each
6 oranges $2.00 per dozen
1 box crackers 2.00 per box
cellophane wrap $.50 each
Note: Each basket has only one of each item in it.
Cost of Goods Sold: $
Suggested selling price: $
The cost of Goods Sold will be $93.5
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The Cost of Goods Sold for one Holiday Basket:
1 basket = $24.00 per dozen
2 lbs. Cheddar cheese = $1.50 per pound
1 canned ham = $60.00 per dozen
3 jars of jelly = $1.00 each
6 oranges = $2.00 per dozen
1 box crackers = 2.00 per box
Cellophane wrap = $.50 each
Now,
Since, Each basket has only one of each item in it.
So, The total cost = $24 + $1.50 x 2 + $60 + $1 x 3 + $1 + $2 + $0.50
= $93.5
Thus, The cost of Goods Sold will be $93.5
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Will mark Brainliest for right answer
Answer:
Toni had the highest score.
Step-by-step explanation:
Terri - 45/50 = 90%
Toni - 92%
Tina - 8/9 = 89%
How do you think increased distance will affect travel time?
You can notice that travel time is afected by the traveled distance. That's because it is required more time to travel longer distances.
For instance, if Elena would live 6 miles to the school, she would take 30min to arrive to school. That is, for greater distances the travel time increases.
Kathleen took a total of 20 quizzes over the course of 4 weeks. After attending 7 weeks of school this quarter, how many quizzes will Kathleen have taken in total?
To determine the number for a unit value the unitary method is used.
The number of quizzes Kathleen will take in 7 weeks is 35.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
Total number of quizzes in 4 weeks = 20
Total number of weeks the school is attended = 7
In order to find total number of quizzes in 7 weeks, apply unitary method to find the number of quizzes per week and then multiply it by 7 as follows,
Since, total number of quizzes in 4 weeks is 20
The number of quizzes in 1 week is 20 / 4 = 5.
Thus, the number of quizzes in 7 weeks is 5 × 7 = 35.
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Match each exponential function with the graph that correctly models the function.
Answer:
Step-by-step explanation:
1) third graph -> the base is 3 so the graph increase
2) first graph -> if x = 0 ; y = -2
(1/3)^0 -3 = 1 - 3 = -2
3) second graph