To find the z-score for a given systolic blood pressure reading, we need to use the z-score formula:
z = (x - mu) / sigma
where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.
In this case, we are given that mu = 121 and sigma = 15. We can use this information to find the z-score for each of the given blood pressure readings:
A. For a blood pressure reading of 142, we have:
z = (142 - 121) / 15
= 21 / 15
= 1.4
Therefore, the z-score for a blood pressure reading of 142 is approximately 1.4, to the nearest tenth.
B. For a blood pressure reading of 130, we have:
z = (130 - 121) / 15
= 9 / 15
= 0.6
Therefore, the z-score for a blood pressure reading of 130 is approximately 0.6, to the nearest tenth.
C. For a blood pressure reading of 103, we have:
z = (103 - 121) / 15
= -18 / 15
= -1.2
Therefore, the z-score for a blood pressure reading of 103 is approximately -1.2, to the nearest tenth.
12. Look at this shape:
Which image
shows a reflection and why?
Answer:
Answer is B.
Step-by-step explanation:
Option A seem to look like a rotation of 180°.
Option B is a reflection across the x-axis.
Option C is a translation shift.
At the city museum, child admission is $5.20 and adult admission is $9.70. On Thursday, 142 tickets were sold for a total sales of $1107.40. How many child tickets were sold that day?
Answer:
Step-by-step explanation:
To be honest I would help but I can't. Although the question looks familiar
find the general solution of the given second-order differential equation. y'' − 10y' + 26y = 0
The general solution of the given second-order differential equation is
y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
In the given question we have to find the general solution of the given second-order differential equation.
The given second-order differential equation is:
y'' − 10y' + 26y = 0
We can write this equation as
d^2(y)/dx^2 − 10dy/dx + 26 = 0
Let d/dx = D
then, d^2/dx^2 = D^2
Now the equation is:
(D^2 − 10D + 26)y = 0
Now solving the equation as a quadratic equation.
m^2 − 10m + 26 = 0
m = [tex]\frac{-(-10)\pm\sqrt{(-10)^2-4\times1\times26}}{2\times1}[/tex]
m = [tex]\frac{10\pm\sqrt{100-104}}{2}[/tex]
m = [tex]\frac{10\pm\sqrt{-4}}{2}[/tex]
m = [tex]\frac{10\pm2i}{2}[/tex]
m = 5±1
Now the general equation for quadratic equation is
y = [tex]e^{at}[/tex]([tex]c_{1}[/tex]cosbt + [tex]c_{2}[/tex]sinbt)
As a = 5 and b = 1
Now the general solution of the given second-order differential equation is y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).
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Michael and Imani go out to eat for lunch if their food cost 25.30 and there is an 8% meals tax how much is the bill rounded to the nearest cent
Answer:
$25.30(0.08) = $2.024. I hope this helped! $27.32 + $4.92 = $32.24 in total! I hope this helped
Step-by-step explanation:
Two companies are trying to sell laptops to a school district. The tables show to total cost for laptops purchased from each of the companies.
Company 1
1=$425
3=$475
5=$525
Company 2
1=$250
3=$350
5=$450
How many laptops would the school district have to purchase for the cost to be the same for both companies?
The school district have to purchase 8 laptops for the cost to be the same for both companies.
What is sequence?
A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is the number of elements.
Given that the company 1 offers:
The cost of 1 laptop is $425.
The cost of 3 laptop is $475.
The cost of 5 laptop is $525.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $50
The company 2 offers:
The cost of 1 laptop is $250.
The cost of 3 laptop is $350.
The cost of 5 laptop is $450.
The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $100
Take the cost as a sequence:
The common difference of first sequence is 50/2 = 25.
The common difference of second sequence is 100/2 = 50.
Assume that the school district needs to buy n computer.
The nth term of a sequence is a + (n - 1)d, where a is the first term, d is common difference.
The nth term of the first sequence is 425 + (n - 1) 25
The nth term of the second sequence is 250 + (n - 1) 50
According to question,
425 + (n - 1) 25 = 250 + (n - 1) 50
425 + 25n - 25 = 250 + 50n - 50
25n - 50n = 250 - 50 - 425 + 25
- 25n = -200
Divide both sides by 25
n = 8
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Braden knows how to sing 6 vocal pieces, thanks to his choir class. Now he's about to start
private lessons. His teacher says he will learn 1 new piece each week.
Write an equation that shows the relationship between the number of weeks Braden takes
voice lessons, x, and the number of pieces he knows, y.
y =
The equation that shows the relationship is y = 6 + x
How to determine the equation that shows the relationship?From the question, we have the following parameters that can be used in our computation:
Initial number of pieces = 6
Additional number of pieces per week = 1
The equation that shows the relationship is represented as
Number of pieces = Initial number of pieces + Additional number of pieces per week * Number of weeks
Substitute the known values in the above equation, so, we have the following representation
Number of pieces = 6 + 1 * Number of weeks
So, we have
Number of pieces = 6 + Number of weeks
Using the representations:
The number of weeks Braden takes voice lessons, x, The number of pieces he knows, y.We have
y = 6 + x
Hence, the equation is y = 6 + x
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a quadratic function can be used to model the height, in feet, of an object above the ground in terms of the time, in seconds, after the object was launched. according to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. based on the model, what was the height, in feet, of the object 1 second after it was launched?
The height of the object 1 second after it was launched is equals to 243.1 feet.
Let the launching velocity /initial velocity = u ft./s
and final velocity = 0 feet/sec , because at the maximum height, the final velocity of launching is '0'.
Maximum height , s = 3136 feet
time, t = 14 sec
Using the Equation of motion,
v² - u² = -2gs
where, v --> final velocity
u --> initial velocity
g --> acceleration due to gravity and it is a constant with value 9.8 m/sec²
s --> distance ( max. height)
plugging all known values in above formula,
0 - u² = -2 (9.8)(3136) = - 61465.6
=> - u² = - 61465.6
=> u² = 61465.6
=> u = √61465.6 = 247.92 ~ 248
=> u = 248 feet/sec
Now, the height, in feet, of the object 1 second after it was launched is
s = ut + (1/2)(-g)t²
=> s = 248(1) + (1/2)(-9.8)(1)
=> s = 248 - 4.9 = 243.1 feet
So, the required height is 243.1 feet.
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combine 3 times j and 16 is 7 times j
Answer:
19 times j
Step-by-step explanation:
To combine 3 times j and 16 is 7 times j, we can add the two expressions together:
3 times j + 16 is 7 times j = (3 + 16) times j = 19 times j
Therefore, the combined expression is 19 times j.
Edgar is putting toys into bags. One bag can hold 6 toys and Edgar has 53 toys. How many bags will Edgar fill? Write the answer as a mixed number AND an improper fraction.
Answer:
[tex]\textsf{Improper fraction}: \quad \dfrac{53}{6}[/tex]
[tex]\textsf{Mixed number}: \quad 8\frac{5}{6}[/tex]
Step-by-step explanation:
Definitions
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.A mixed number is a number consisting of a whole number and a proper fraction.A proper fraction is a fraction where the numerator is less than the denominator.If each bag holds 6 toys and Edgar has 53 toys, to find how many bags Edgar will fill, divide 53 by 6.
Improper fractionTo write this as an improper fraction, place 53 as the numerator and 6 as the denominator:
[tex]\implies \dfrac{53}{6}[/tex]
As 53 is a prime number, its only factors are 1 and 53. Therefore, the improper fraction cannot be reduced any further.
Mixed numberRewrite 53 as the sum of 48 and 5:
[tex]\implies \dfrac{53}{6}=\dfrac{48+5}{6}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:[/tex]
[tex]\implies \dfrac{48}{6}+\dfrac{5}{6}[/tex]
Divide 48 by 6:
[tex]\implies \dfrac{6 \cdot 8}{6}+\dfrac{5}{6}[/tex]
[tex]\implies 8+\dfrac{5}{6}[/tex]
Write as a mixed number:
[tex]\implies 8\frac{5}{6}[/tex]
what would be the null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup
The null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup is Divorce Opinions and Gender I.
We introduce the results of a
May 2010 Gallup poll of 1029 US adults. When asked if they view divorce as “morally acceptable”,
71% of the men and 67% of the women in the sample responded yes. In the test for a difference in
proportions, a randomization distribution gives a p-value of 0.165. Does this indicate a significant
Solution
If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not
reject H0 : pf = pm. This means the data do not show significant evidence of a difference in the
proportions of men and women that view divorce as “morally acceptable”
Solution
(a) The p-value (0.003) is small so the decision is to reject H0 and conclude that the mean recall
for sleep (¯xs = 15.25) is different from the mean recall for caffeine (¯xc = 12.25). Since the mean
for the sleep group is higher than the mean for the caffeine group, we have sufficient evidence to
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Remainder Theorem, (refer to attached image) please help
The type of reasoning used to prove the remainder theorem is; Deductive reasoning
How to interpret Logical Reasoning?Logical reasoning involves using a given set of facts or data to deduce other facts by reasoning logically
There are 4 major types of reasoning here and they are;
1) Deductive reasoning; This is defined as a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.
2) Inductive reasoning; This is a method of drawing conclusions by going from the specific to the general.
3) Abductive reasoning; This is defined as a syllogism in which the major premise is evident but the minor premise and therefore the conclusion only probable.
4) Reasoning by analogy; This involves using a well known situation to assert something about a less well understood situation
In this case, we are told that since (x - 5) is a factor of the polynomial x² - 25, if he performs the long division (x² - 25) ÷ (x - 5), the remainder would be zero.
Now, this is an example of deductive reasoning because it has used the initial premise to draw a conclusion on the remainder.
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Which of the following is not a type of graph?EulerHamiltonianTreePath
Answer:
Step-by-step explanation:
Answer = D Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler. 32) Which of the following is not a type of graph ? Answer = D Explanation:Path is a way from one node no another but not a graph.
Observation, experimentation, and mathematics, in combination, produce reliable results. This statement describes a development of thought during which period?.
This statement describes a period known as the Scientific Revolution.
The Scientific Revolution: What Was It?
The 16th and 17th centuries saw a radical shift in scientific ideas that is known as the Scientific Revolution.
During the Scientific Revolution, a new understanding of nature replaced the Greek perspective that had dominated science for nearly two thousand years.
The Scientific Revolution was absent?
The Enlightenment, an intellectual and social movement, was influenced by the scientific revolution, which started in Europe at the end of the Renaissance and lasted until the late 18th century.
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In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. the equation was y=10+0.9x where y is the final exam score and x is the score on the first test. Bill scored a 90 on the first test and his residual was -2. what was his score on the final exam?
a. 89
b. 91
c. 93
d. 90
e. not enough information
Answer:
E
Step-by-step explanation:
Based on the given linear regression equation, Bill's score on the final exam would be calculated as follows:
y = 10 + 0.9 * 90 = 98
Austin is going to see a movie and is taking his 5 kids. Each movie ticket costs $14
and there are an assortment of snacks available to purchase for $5 each. How much
total money would Austin have to pay for his family if he were to buy 7 snacks for
everybody to share? How much would Austin have to pay if he bought a snacks for
everybody to share?
Total cost with 7 snacks:
Total cost with a snacks:
The total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.
What is a numerical expression?
Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
Here, we have
Given,
Austin is going to see a movie and is taking his 5 kids.
Each movie ticket costs $14 and there is an assortment of snacks available to purchase for $5 each.
The total amount Austin to pay if he were to buy 7 snacks for everybody to share is,
= (14×7) + (3×7)
= 98 + 21
= $119
Hence, the total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.
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Jonah needs to determine the dimensions of a rectangular poster that will cover an area represented by
7x² + 3x - 10. Which of the following expressions is equivalent to the area of the rectangular poster?
A (x+1)(7x-10)
B (x-1)(-7x+10)
C(x-1)(7x+10)
D(x-7)(x+10)
E(7x-1)(x+10)
Answer:
The correct answer is A (x+1)(7x-10).
Step-by-step explanation:
To determine the dimensions of a rectangular poster that will cover an area represented by 7x² + 3x - 10, we need to find the factors of the expression 7x² + 3x - 10 that will give us the length and width of the poster.
One way to do this is to factor the expression 7x² + 3x - 10 using the difference of squares method. We can write the expression as follows:
7x² + 3x - 10 = (7x² + 3x) - 10
To factor (7x² + 3x) - 10, we can write the expression as the difference of squares:
(7x² + 3x) - 10 = (7x² + 3x + 10) - (10 + 10)
To simplify the expression, we can complete the square for the terms in parentheses:
(7x² + 3x + 10) - (10 + 10) = (7x² + 3x + 10) - 20
To complete the square, we need to add and subtract the square of half the coefficient of the x term, which is (3/2)² = 9/4. We can rewrite the expression as follows:
(7x² + 3x + 10) - 20 = (7x² + 3x + 10 + 9/4) - (20 - 9/4)
To simplify the expression, we can factor the terms in parentheses:
(7x² + 3x + 10 + 9/4) - (20 - 9/4) = [(7x² + 3x + 10 + 9/4) - (20 - 9/4)]
To simplify the expression further, we can factor out a common factor:
[(7x² + 3x + 10 + 9/4) - (20 - 9/4)] = (x + 1)(7x - 10)
From the given options, the expression that represents the area of the rectangular poster is (x+1)(7x-10), which is equivalent to 7x² + 3x - 10. We can verify this by multiplying (x+1)(7x-10) to get 7x² + 3x - 10. Therefore, the correct answer is A (x+1)(7x-10).
Find the inverse of the function.
y = 3x + 3
Write your answer in the form ax + b. Simplify any fractions.
y =
Submit
At the beginning of her enior year maria received a $5,000 ubidized loan and a $4,500 unubidized loan with an apr of 5. 5%. If maria begin making payment on her loan 6 month after graduation, how much interet will he owe to the nearet dollar?
The amount of interest Maria owes after 6 month of graduation, if she take a subsidized loan of $5,000 and unsubsidized loan of $4,500 is $508.75.
Therefore, the answer is $509.
Subsidized loan
Here, the time period is considered only after graduation, so time period is 6 months, that is 0.5 year. We know simple interest formula where P is the principal amount, r is annual interest rate and n time period in years.
I = P×r×n
Therefore I₁ = 5000 × 0.055 × 0.5
I₁ = 137.5
Unsubsidized loan
Here the time period is considered from the time the loan taken, so time period is one year of graduation plus 0.5 year, i.e. n = 1.5yrs.
Therefore, I₂ = 4500 × 0.055 × 1.5
I₂ = 371.25
Therefore total interest for both the loan is
I = I₁ + I₂
I = 137.5 + 371.25
I = 508.75
I ≈ $509
--The question is incomplete, the complete question is as follows--
"At the beginning of her senior year Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.5%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?"
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Please help me respond this
Answer:i don't know thanks for the brainy money tho
Step-by-step explanation:
a data display showing the number of children per household in the us is strongly skewed right. the mean number of children per household is 3. what is a possible value for the median? check all that apply.
If the data display is strongly skewed right, it means that there are relatively more households with a higher number of children compared to households with a lower number of children. This means that the median value is likely to be higher than the mean value of 3 children per household.
Possible values for the median could be 4, 5, or even higher. It is not possible to determine the exact value of the median without more information about the distribution of the data. However, it is reasonable to assume that the median could be 4 or 5 children per household in this case.
In quantitative research, what is data display?The use of visual representations to organize, summarize, simplify, or alter data aids in the presenting of judgments and conclusions. Data visualizations like matrices and networks are frequently used to improve data analysis; they are more frequently found in quantitative research than in qualitative ones.
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Answer:
A) 0
B) 1
C) 3
Step-by-step explanation:
edge 2023
Identify the function family to which f belongs. Then identify the domain and range of f.
a. What type of function is shown?
b. What is the domain:
c. What is the range:
-4 -3 -2 -1
2
4
-5
-6
y
2 3 4 x
Answer:A function can be transformed to another through dilation, reflection, translation, and rotation. Belongs to the quadratic family. The following is the comparison of and its parent function
Both functions are quadratic
The parent function is vertically stretched by 2, rotated along the x-axis and then translated up by 3 units.
Step-by-step explanation:
I don't think this is right
Two number have a difference of 20. How do you find the number if the um of their quare i a minimum?
The first and second numbers are -10 and 10, respectively. because their difference is zero
What is unitary method?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.
Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.
According to our question-
Let us consider that first number is x and second number is y.
Hence, The first and second numbers are -10 and 10, respectively.
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ƒ(x) = √−2x What is the domain of f?
The domain of the function is all negative real number and zero.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The given function
ƒ(x) = √−2x
The domain of the expression is all real numbers except where the expression is undefined.
And here, when x is positive real number then field changes to complex.
That means the function is undefined in real field when x is not negative or zero.
Therefore, the domain of the function is all negative real number and zero.
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two buses leave towns miles apart at the same time and travel toward each other. one bus travels slower than the other. if they meet in hours, what is the rate of each bus?
two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus = 62 mph
let first bust travels at x mph
then, 2nd but will travel at ( x - 10) mph
distance travelled by first bus in 2 hours = 2x
distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20
distance between the two is 268 miles
so we can write
2x + 2x - 20 = 268
4x = 288
x = 288 / 4 = 72 mph
rate of first bus = 72 mph
and second bus = 72 - 10 = 62 mph
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950.95 written in expanded form
Answer:
(9 x 100) + (5 x 10) + (0 x 1) + (9/10) + (5/100)
hope this helps brainliest <3
Answer:
Step-by-step explanation:
Which of the following statements is true regarding a scatter diagram?
a. It provides very little information about the relationship between the regression variables.
b. It is a plot of the independent and dependent variables.
c. It is a line chart of the independent and dependent variables.
d. It has a value between -1 and +1.
e. It gives the percent of the variation in the dependent variable that is explained by the independent variable.
Option B is correct. It is a plot of the independent and dependent variables.
A scatter diagram is a type of plot or graph that uses Cartesian coordinates to display the values of two variables for a set of data. It is a simple yet powerful way to visualize the relationship between two variables.
The points on the plot represent the values of two variables, the independent variable (X-axis) and the dependent variable (Y-axis). Scatter diagrams provide a visual representation of the relationship between the two variables, which makes it easier to identify patterns such as linear or non-linear relationships.
They also can show correlations, or lack thereof, between two or more variables. Additionally, scatter diagrams can provide insight into the strength of the relationship between the two variables as well as how much of the variation in the dependent variable is explained by the independent variable. For example, a correlation coefficient of 1 indicates a perfect linear relationship, while a correlation coefficient of 0 indicates no relationship between the two variables.
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PLEASE HELP FAST ILL GIVE BRAINLIEST IF CORRECT!!!!
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
A. One solution
B. Infinitely many solutions
C. Two solutions
D. No solutions
Answer: (A) One solution
Please help!! 45 points!!
A ball is projected into the air. Its height at time, t, is given by the equation h=-16t^2 + 100t + 2. When will the ball return to the ground?
A.0.02 sec
B. 6.3 sec
C. 6.5 sec
D. 16 sec
Answer:
The ball will return to the ground at t = 16 seconds, so the correct answer is D.
Step-by-step explanation:
To find when the ball will return to the ground, we need to find the time at which the ball's height is equal to 0. We can do this by setting the height equation equal to 0 and solving for t.h = -16t^2 + 100t + 2
0 = -16t^2 + 100t + 2
-2 = -16t^2 + 100t
-0.125t = -2
t = 16
Answer:
B. 6.3 sec
Step-by-step explanation:
To find the time when the ball will return to the ground, we need to find the value of t when h is equal to 0 (since height = 0 means the ball is on the ground). We can do this by substituting 0 for h in the given equation and solving for t.
So, let's start by substituting 0 for h:
h = -16t^2 + 100t + 2
0 = -16t^2 + 100t + 2
-16t^2 + 100t + 2 = 0
This is a quadratic equation, which we can solve using the quadratic formula:
t = (-100 +/- sqrt(100^2 - 4(-16)(2)) ) / (-2(-16))
t = (-100 +/- sqrt(10000 + 128)) / 32
t = (-100 +/- sqrt(10128)) / 32
t = (-100 +/- 100.64) / 32
t = (200.64) / 32
t = 6.3125
Since the ball is projected into the air and then falls back down to the ground, the time when it returns to the ground must be a positive value. Therefore, the solution to the problem is t = 6.3 sec
The football team ha a total of 50 jerey. There are 20 medium jerey. What percent of the jerey are medium ize jerey?
the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
In order to calculate the percentage of medium jerseys, we must divide the total number of medium jerseys (20) by the total number of jerseys (50).
To express this as a percentage, we must multiply the result by 100. Therefore, 20 ÷ 50 = 0.4 and 0.4 x 100 = 40%. Thus, 40% of the jerseys are medium size. the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%
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need help with problem!
Whats the problem put a proper question