The area of the rectangle is given by the formula below:
A = 18x^2 - 27x + 7
What is the area of the rectangle?For a rectangle of width W and length L, the area is given by the formula:
A = W*L
Here we know that the dimensions of a rectangle are 6x-7 and 3x-1, then we can define:
L = 6x - 7
W = 3x - 1
Replacing that in the area formula above we will get:
A = (6x - 7)*(3x - 1)
Now we can expand that product:
A = (6x)*(3x) + (6x)*(-1) + (-7)*(3x) + (-7)*(-1)
A = 18x^2 - 6x - 21x + 7
A = 18x^2 - 27x + 7
That is the formula for the area in terms of x.
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The mean systolic blood pressure of people in the U.S. is
124
124 with a standard deviation of
18
18. Assume that systolic blood pressure follows a normal distribution. Round your answers to one decimal. Use the 68-95-99.7 Rule to answer the following questions.
a) What percentage of the people in the U.S. have systolic blood pressure between
106
106 and
124
124?
%
%
Preview
b) What percentage of the people in the U.S. have systolic blood pressure between
88
88 and
160
160?
%
%
Preview
c) What percentage of the people in the U.S. have systolic blood pressure between
70
70 and
124
124?
%
%
Preview
d) What percentage of the people in the U.S. have systolic blood pressure above
160
160?
%
%
The percentages, using the Empirical Rule, are given as follows:
a) Between 106 and 124: 32%.
b) Between 88 and 160: 95%.
c) Between 70 and 124: 49.85%.
d) Above 160: 2.5%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The mean and the standard deviation in this problem are given as follows:
Mean of 124.Standard deviation of 18.Considering the symmetry of the normal distribution, to facilitate the calculations, we have that:
49.85% of the measures are between 70 and 124.47.5% of the measures are between 88 and 124.32% of the measures are between 106 and 124.32% of the measures are between 106 and 142.47.5% of the measures are between 124 and 160.49.85% of the measures are between 124 and 178.160 is two standard deviations above the mean, hence the percentage above it is of:
2.5%.
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A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then
returning. The total time for the trip was 7.0 hours. Use this information to find the speed of the current.
What is speed of the current is miles per hour?
The speed of the current is equal to 8 miles per hour.
How to calculate the speed of the current?Mathematically, speed of any physical object can be calculated by using this formula;
Speed = distance/time
Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:
Speed downstream = 14 + c.
Speed upstream = 14 - c.
Additionally, the total time would be given by:
Total time = total distance/speed
Time upstream + time downstream = 6.5 hours
33/(14 - c) + 33/(14 + c) = 7.0
Multiplying both sides of the equation by (14 - c)(14 + c), we have:
33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)
462 + 33c + 462 - 33c = 7.0(196 - c²)
924 = 7.0(196 - c²)
Dividing both sides of the equation by 7.0, we have:
132 = 196 - c²
Speed of the current, c² = 196 - 132
Speed of the current, c² = 64
Speed of the current, c = √64
Speed of the current, c = 8 miles per hour.
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What is the correct answer
Answer: See coordinate graph below.
Step-by-step explanation: The black point is the original point and the red point is the reflected point.
Ordered pair of the reflected point:
A': (1, -4)
Let me know if this is right! :)
24.) MULTIPLE FORMS Write the decimal 0.5 in two ways. One with a denominator of 10 and one
with a denominator of 100.
Answer:
A denominator of 10: 5/10
A denominator of 100: 50/100
Pls help question 9 and 10
The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.
AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.
In the given figure FE║GE means FE is parallel to GE.
so ∠EFS = ∠HGS
and ∠FES = ∠GHS
also ∠S is common for both.
If two triangles are similar then ratio of corresponding sides are also same.
So, by applying this
[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]
54/24 = FE/20
( 54*20 ) / 24 = FE
FE = 45m.
Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.
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F(n)= 3n -4 find term 3 of the explicit arithmetic sequence
The third term will be 5 in the explicit arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
The explicit formula of an arithmetic sequence is given in the question as:
F(n) = 3n -4 ....(i)
To determine the term 3.
Substitute the value of n = 3 in equation (i),
T₃ = 3(3) - 4
T₃ = 9 - 4
Apply the subtraction operation,
T₃ = 5
Therefore, the third term will be 5 in the explicit arithmetic sequence.
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2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.
How to determine the weight?Let x represent the weight of Cooper
Let x +25 represent the weight of Daisy
Let 3x -20 represent the weight of Luna
Hence,
x + (x +25) + (3x -20) = 175
5x +5 =175
Combine like terms
5x = 175 -5
5x =170
Divide both side by 5x
x = 170/5
x =34
Weight of Luna
3x -20 where x= 34
3(32) -20
= 102 -20
= 82 pounds
Therefore the correct option is D.
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Show, by shading on the grid, the region defined by all three of the inequalities
x ≤ 5 y ≥ 3 y ≤ x
Answer:
See below
Step-by-step explanation:
The area (triangle) marked 'x' in the diagram below
A survey asked 300 students to choose their favorite type of movie.
The results are shown in the following table.
(a) Find the percentage for each type of movie.
Type of movie
Action
Comedy
Drama
Thriller
Number of
students
27
42
120
111
Percentage
1%
%
%
%
X
5
Answer:
300/100%=3%
Step-by-step explanation:
sorry, can't explain.Ihave class tomorrow
Write an exponential function in the form y = ab^x that goes through points (0, 14)
and (4,8750).
The exponential function will be written as y = 14⁰.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,
[tex]y = ab^x \\[/tex]
14 = ab⁰
a = 14
The equation will be written as,
y = 14b⁰
y = 14⁰
Therefore, the exponential function will be written as y = 14⁰.
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can you explain thia
a sequence is defined by a term to term rule
iteration help please
By the sequence of term to term rule the value of : a) [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4 b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19 c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .
What is the term to term rule like for you?
Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to
[tex]$$\mathrm{u}_0=1$$[/tex]
The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3
We have to simply put the value in their places to get the proper answer -
a). Put the [tex]$u_{n+1}=u_1$[/tex]
n+1 = 1 ⇒ n = 0
put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3
we wil get
[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4
b). Put the [tex]$u_{n+1}=u_2$[/tex]
n + 1 = 2 => n = 1
put n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3
we wil get:
[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19
c). Put the [tex]$u_{n+1}=u_3$[/tex]
n + 1 = 3 => n = 2
Put n=2 in the formula+3
we wil get :
[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364
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Question content area top Part 1 What is the constant of proportionality in the equation y=−7.48x?
The constant of proportionality of the equation y =−7.48x is - 7.48.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent
In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.
Therefore, a proportional relationship is one in which two quantities vary directly with each other.
Hence, in mathematical form,
y ∝ x
y = kx
where
k = constant of proportionalityy varies directly as the variable x.
In the equation,
k = - 7.48
Therefore, the constant of proportionality is - 7.48.
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What is the y-intercept of x = -4?
Answer:
DNE
Step-by-step explanation:
You want to know the y-intercept of x = -4.
Y-interceptThe y-intercept is the point where a graph crosses the y-axis.
The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.
There is no y-intercept. It does not exist (DNE).
Five twelfths of the marbles in a bag are blue. What fraction of the marbles are not blue?
Answer:
7/12
Step-by-step explanation:
12/12 - 5/12 = 7/12
At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation:
Question
In 8 years, Estelle's bank account earned $1,270
simple interest at 2.5%. How much had she
deposited in the account?
Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
According to the question,
We have the following information:
In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.
Now, let's take the principal amount to be $x.
We know that the following formula is used to find simple interest:
Simple interest = (principal*rate*time)/100
(x*2.5*8)/100 = 1270
Using the cross multiplication method:
20x = 127000
x = 127000/20
x = $6350
Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
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20. In Problem 14 in Chapter 11, we described a study
showing that students are likely to improve their test
scores if they go back and change answers after
reconsidering some of the questions on the exam
(Johnston, 1975). In the study, one group of students
was encouraged to reconsider each question and
to change answers whenever they felt it was appropri-
ate. The students were asked to record their original
answers as well as the changes. For each student, the
exam was graded based on the original answers and on
the changed answers. For a group of n = 40 students,
suppose that 26 had higher scores for the changed-
answer version and only 14 had higher scores for
the original-answer version. Is this result significantly
different from chance? Use a two-tailed test with
α = .01.
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
$69
$90
$420
$1,080
Answer: The answer to this question is $90.
Step-by-step explanation:
The Simple interest is $90.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.
Given:
P= 1500
R = 12%
T= 6 month = 1/2 year
Using, formula of Simple Interest
I = P x R x T /100
I = 1500 x 12 x 1/ 2x100
I = 18000/200
I = 90
Hence, the interest is $90.
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Johnny is 5 years younger than twice Bobby's age. If the sum of thier ages is over 66 years.
What is the Johnny's minimum age?
The minimum age of Johnny is 21 as calculated by linear inequality.
Let Johnny 's age be x.
hence bobby's age = (x+5)/2
Now the sum of their ages is over 66 years.
So we will set an inequality to find the minimum age of Johnny.
x + (x+5)/2 > 66
or, 2x + x + 5 > 66
or, 3x > 61
or, x > 20 1/3
Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.
In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:
A is smaller than b, as shown by the symbol a < b.
When the expression a > b is employed, it means that a is greater than b.
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Find the Average Rate of Change (AROC) of y = 4(1/2)^x over the interval [-2, 0].
a) 6
b) -6
c) 4
d) -4
Answer:
b) -6------------------------
Find the value of the function at the endpoints of the given intervalx = - 2 ⇒ y = 4(1/2)⁻² = 4(2)² = 4(4) = 16x = 0 ⇒ y = 4(1/2)⁰ = 4(1) = 4Average rate of change isChange in y / change in x =(4 - 16)/(0 - (-2)) = - 12 / 2 = - 6Correct choice is B.
Answer:
b) -6
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given the interval is [-2, 0]:
a = -2b = 0Substitute the endpoints of the interval into the function and solve:
[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]
Question
Find the rate if a principal of $1,100 earned $1,089 interest in 12
years.
Answer:
Step-by-step explanation:
Intrest = PRT\100
$1089. =. ($1100x12xR)\100
$1089. = 132R
Divide through by 132.
R. =. 8.25%
tenths hundreths thousands
1. 67.925
2. 182.0051
3. 39.1432
4. 85. 0267
5. 97.7352
Answer:
Step-by-step explanation:
1) sixty-seventh and nine hundred and twenty-five thousands
2)one-eighty two and fifty-one thousands
3)thirty-nine and thousand four thirty two thousands
4) eighty five and two sixty seven thousands
5) ninety seven and seven thousand and three-fifty two thousands
Use the properties of congruent triangle to find the value of x and y. Be sure to show all your work
Answer:Angles in a triangle may or may not be congruent.
The values of x and y are 90 and 47, respectively.
From the figure, we have:
This means that, angle x is a right-angle.
So, we have:
Triangle ABC is an isosceles triangle.
So, we have:
The measure of y is then calculated as:
--- sum of angles in a triangle
This gives
Subtract 137 from both sides
Hence, the values of x and y are 90 and 47, respectively.
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Step-by-step explanation:
A school is arranging a field trip to the zoo. The school spends 895.28 dollars on passes for 36 students and 2 teachers. The school also spends 321.84 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units
Answer:
I think B. 3.85 units
Step-by-step explanation:
Is 4.5 greater, less than, or equal to 4 and 1/2
Answer:
equal to
Step-by-step explanation:
4 + 1/2= 4+ 0.5= 4.5
4.5=4.5
Pedro has $18 to spend at the grocery store. His mother wants him to use the money to buy fruit. Apples cost $2 a pound and pears cost $3 a pound
Answer:
Pedro can buy 4 pounds of pears and 3 pounds of apples.
Step-by-step explanation:
Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.
$2×3lb + $3×4lb=$18
Questions
Surds exam questions
Q1. Express √3+√12 in the form a√3 where a is an integer.
Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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