Lilliana is training for a marathon. She runs the same distance every day for a week on Monday,
Wednesday, and Friday, she runs 2 laps on a running trail and then runs 6 more miles. On Tuesday and
Sunday, she runs 4 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How
many laps does Lilliana run on Saturday?
Answer: 6 miles
Step-by-step explanation:
WEDNESDAY + FRIDAY (# OF MILES)
The Miles Covered by Each Lap = 3x
The Miles on Top of That = 6
TUESDAY + SUNDAY (# OF MILES)
The Miles Covered by Each Lap = 5x
The Miles on Top of That = 2
You want to now put that into an equation! Therefore, you want to put the number of miles from Wednesday and Friday on one side and the number of miles from Tuesday and Sunday on the opposite side.
SOLVING EQUATION FOR MILES PER LAP
Step 1) 3x + 6 = 5x + 2
given equation from what we put together.
Step 2) -3x + 3x + 6 = 5x + 2 -3x
subtract 3x from both sides.
Step 3) -2 + 2x + 2 = 6 -2
subtract 2 from both sides.
Step 4) 2 × x = 4
divide both sides by 2 because you want to put the variable (x) on one side.
Step 5) x = 2 miles for each lap
Now you want to go look back at the equation and plug in 2 for the variable x.
Step 6) 5 ×2 + 2 = 12
PEMDAS!
Step 7) 12 ÷ 2 = 6
SHE RUNS 2 MILES ON SATURDAYS!
A= 1,321 +0.3433m
The equation above can be used to estimate the body surface area A, in square centimeters, of a child with mass
m, in grams, where 3,000 sms 30,000 Which of the following statements is consistent with the equation?
O a
A. For each increase of 1 gram in mass, A increases by approximately 0.3433 square centimeter.
Ob
B. For each increase of 0.3433 gram in mass, A increases by approximately 1 square centimeter.
Ос
C For each increase of 1 gram in mass, A increases by approximately 1,321 square centimeters.
Od
D. For each increase of 1,321 grams in mass, A increases by approximately 1 square centimeter.
Answer:
Option A: For each increase of 1 gram in mass, A increases by approximately 0.3433 square centimeter.
Step-by-step explanation:
We are given the function;
A= 1321 + 0.3433m
To find the rate of increase of the area, we will find the derivative of the function. Thus;
dA/dm = 0.3433
This means that the area increases at the rate of 0.3433 Sq.metre for each additional 1 gram added to the mass.
Looking at the given options, the one that corresponds to our answer is Option A
B. In three to five sentences, write the significance of function in showing real-life
situations,
South High School began the school
year with 1125 students. They have
lost 4% of their student body due
to attrition.
How many students has South
High School lost to attrition?
Answer:
45
Step-by-step explanation:
1125 students×.04 attrition =45 students lost
The following is an excerpt from a soccer magazine. Read and answer the question The ball should weigh between 410–450 g (14–16 oz), with a circumference of 68–70 cm (27–28 in). The ball's weight must be in the range of 410 to 450 g (14 to 16 oz) and inflated to a pressure of 0.6 and 1.1 bars (8.7 and 16.0 psi) at sea level. Create a compound inequality for the weight using min and max weight values, leave units out, just the numerical answer.
Answer:
A) 410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70
B) 410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1
Step-by-step explanation:
In the first statement we are told that the ball should weigh between 410–450 g (14–16 oz), with a circumference of 68–70 cm (27–28 in).
If the weight is x, it means we have the inequality as;
410 ≤ x ≤ 450
If the circumference is denoted as y, we have;
68 ≤ y ≤ 70
Compound inequality is when we join two inequalities with the word "OR" or the word "AND.
Thus, the compound inequality is;
410 ≤ x ≤ 450 AND 68 ≤ y ≤ 70
Similar to he first statement, in the second statement, we have;
410 ≤ x ≤ 450
If the inflated pressure is denoted by z, then we have;
0.6 ≤ x ≤ 1.1
Like in the first statement, the compound inequality can be represented as;
410 ≤ x ≤ 450 AND 0.6 ≤ x ≤ 1.1
What is the least common multiple of six and eight?
Answer:
24
plz mark me as brainliest :DD
Answer:
The LCM for 6 and 8 = 24
Step-by-step explanation:
Because 24 is the first multiple they have in common.
6 | 8
12| 16
18 | 24 <-- 24
24 | 32
^
24 Least Common Multiple
Researchers tracked 2668 people from early childhood through adulthood and found that 13-year-olds who are frequent
targets of bullies were three times more likely than their non-victimized peers to be depressed later as adults.
Identify the population, sample, and variables for the study.
Answer:
Step-by-step explanation:
(A) The population is the 2,668 people who were tracked from early childhood to adulthood.
(B) The sample comprised all 13-year olds within the population. Since the members of the population started out as kids (and later became adults), the sample was inclusive of all 2,668 individuals but only at the age of 13. That is where the focus was; at the age of 13.
The study then proceeded to divide them into two groups - the experimental group (13 year olds who were frequent targets of bullies) and the non-experimental group (13 year olds who were not frequent targets of bullies).
(C) The variables in this study are:
- 13 year olds who were frequent targets of bullies
- 13 year olds who were not frequent targets of bullies
- Adults (from the same population who were once 13 year olds) with depression
- Adults (from the same population who were once 13 year olds) without depression.
NOTE HOWEVER that the degree of bullying each teenager faced and the magnitude of depression each adult faced, can be gotten from the above variables; when they assume a figure or number which can be high, low or medium.
What formula is used to
determine the expected value for a variable?
The data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. What is the interquartile range of the data? 14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28 12 16 22 28
Answer:
The interquartile range of the data is 12
Step-by-step explanation:
Data : 14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28 12 16 22 28
Data in ascending order : 12 ,14 ,15 ,16 ,16 ,19 ,21 ,22 ,22 ,25 ,27 ,28 ,28 ,30 ,32
Lower quartile :12 ,14 ,15 ,16 ,16 ,19 ,21
Q1 is the median of lower quartile
n = 7
Median =[tex]\frac{n+1}{2} \text{th term}=\frac{7+1}{2}=4 \text{th term}[/tex]=16
Upper quartile :22 ,25 ,27 ,28 ,28 ,30 ,32
Q3 is the median of upper quartile
n = 7
Median =[tex]\frac{n+1}{2} \text{th term}=\frac{7+1}{2}=4 \text{th term}[/tex]=28
IQR = Q3-Q1=28-16= 12
Hence the interquartile range of the data is 12
Answer:
A: 12
Step-by-step explanation:
edg2020
2 + (-2) = 0 0
What property of addition ?
Answer:
Associative I believe
Step-by-step explanation:
The inside of an oven is set to rise to a temperature of 298°F. So far it has risen 76% If this amount.
Which would be the best way to estimate the number of degrees Fahrenheit the inside of the oven has risen so far?
Answer:
226.48°F
Step-by-step explanation:
Temperature of the oven = 298°F
if it has risen 76% of this amount so far, the number of degrees Fahrenheit the inside of the oven has risen so far can be expresses as:
= 76% of 298
= 76/100 * 298
= (76*298)/100
= 0.76*298
= 226.48°F
The temperature inside the oven so far is 226.48°F
You have $8.33. You buy 4 items that cost $0.63 each. How much money do you have left?
Answer:
$5.81
Step-by-step explanation:
$0.63×4=$2.52
$8.33-$2.52=$5.81
Let M = 18,526.6 find the smallest power of 10 that will exceed M
A. 10^6
B. 10^ -1
C. 10^5
How do you write binomial expansions?
Answer:
The expression having two terms is called binomial expression.
we can write binomial expression by using two terms. For example: a+b , 2x+5, etc.
what does the variable, r, stand for in the equation 16- r/7 = 21
Answer:
R stands for 6
Step-by-step explanation:
Help!!!!!!!Plz!!!!!!!
Answer:
I'm so confused
Step-by-step explanation:
How do you find the slope-intercept form from two points?
Answer:
Rise over run.
Step-by-step explanation:
If you have learned rise over run you will get it.
A soup recipe makes 6 cups. How many people does it serve if each serving is of a cup
Answer:
8
Step-by-step explanation:
The blue dot is at what value on the number line?
?
3
1
Answer:
5
Step-by-step explanation:
count
A human gene carries a certain disease from the mother to the child with a probability rate of 39%. That is, there is a 39% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. Round to the nearest thousandth.
Answer:
[tex]Probability = 0.023[/tex]
Step-by-step explanation:
Given
Represent the given probability with P(Gene)
[tex]P(Gene) = 39\%[/tex]
[tex]Children = 4[/tex]
Since all 4 children get the disease, the required probability is calculated as thus:
[tex]Probability = P(Gene)^4[/tex]
[tex]Probability = 39\%^4[/tex]
Convert % to decimal
[tex]Probability = 0.39^4[/tex]
[tex]Probability = 0.02313441[/tex]
[tex]Probability = 0.023[/tex] Approximated
Owen earns a base salary of $925 per month as a salesman. In addition to his salary, he earns $85 per product that he sells. If his goal is to earn more than $4,500 per month, how many products does he need to sell? what would be the problem and solution?
Answer:
43
Step-by-step explanation:
If b^2 = 25 then b= Answer it please
Answer:
b = 5
mark me as brainliest plz!! :DD
Which statement about residual plots is not true?
A. If there is an obvious pattern, the model is probably reasonable.
B. The vertical axis shows residuals.
C. The x-axis appears in the middle of the graph.
D. The sum of the residuals is 0.
Answer:
Step-by-step explanation:
d
Answer:
A
Step-by-step explanation:
2(x-3)=x-5+x plz help
Answer:
x is undefined
Step-by-step explanation:
Simplify the expression, we get
2x-6=2x-5
This will not work
There are no solutions
Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice per year. Use a Poisson process to model the phenomenon. (a) Given that 3 events have occurred in the first half of the year, what is that probability that 3 events will happen in the rest of the year? (b) How many radio blackouts do you expect to see in two years? (c) Starting from now, how long must we wait so that the probability of seeing the next radio blackout is at least 0.5? (d) Find the probability that the time to the 4th blackout is at most 2 years.
Answer:
a. P(x = 3) = 0.061313
b. The expected number of radio blackouts = 4
c. It is not possible to determine the next radio blackout
d. P(x = 4) = 0.19537
Step-by-step explanation:
From the given information:
Using a Poisson process to model the phenomenon:
Since minor radio blackouts occur, on average, twice per year.
Then:
[tex]\lambda = 2 \ years[/tex]
From question (a)
time t = 1/2 (i.e half of the year)
Let x be the random variable that denotes the probability that 3 events will happen in the rest of the year.
Then:
[tex]P(x = 3) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!}[/tex]
[tex]P(x = 3) = \dfrac{e^{-2* 0.5} \times (2 * 0.5)^3}{3!}[/tex]
P(x = 3) = 0.061313
b).
The number of radio blackouts we expect to see in two years can be estimated as follows:
we know that:
t = 2 years
E(x) = λ × t
E(x) = 2 × 2
E(x) = 4
The expected number of radio blackouts = 4
c).
The amount of time we need to wait given that the probability of seeing the next radio blackout is at least 0.5 is as follows:
Here, the time (t) = ???
Thus:
P(x =1) = 0.5
[tex]P(x = 1) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5[/tex]
[tex]\dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5[/tex]
Thus, it is not possible to determine the probability (50%) of seeing the next radio blackout.
d)
The probability that the time to the 4th blackout is at most 2 years can be computed as follows:
Here;
x =4 , t = 2
Thus:
[tex]P(x = 4) = \dfrac{e^{-4 } \times (4)^4}{4!}[/tex]
P(x = 4) = 0.19537
7th grade math help me plzzz
Answer:
a. -7 + 3
b. draw 7 negatives + 7 positives
Step-by-step explanation:
Answer:
3.a) -7 + 3
3.b) 4
I hope this helps!
A large brick oven takes 64 minutes to cook 16 pizzas. How long would it take to cook two pizzas?
Answer:
It would take 8 minutes to cook 2 pizzas in a brick oven.
Step-by-step explanation:
Answer:
It would take 8 minutes to cook 2 pizzas in a brick oven.
Explain how solving -7y > 161 is different from solving 7y > -161.
Answer:
When the coefficient (number before the variable) is negative, you have to switch the inequality symbol after you divide.
Answer:
EDGE 2020
Step-by-step explanation:
Sample response: Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>
Look at the graph and choose the correct answer.
In a certain college,20% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that exactly 7 belong to an ethnic minority?
Answer:
0.000786432
Step-by-step explanation:
In a certain college,20% of the physics majors belong to ethnic minorities
The proportion p = 20%
= 0.2
q = 1 - 0.2 = 0.8
1f 10 students are selected at random from the physics majors
n = 10
x = 7
The formula for Binomial Probability is
= nCx × p^ x × (1−p)^ n−x .
= 10C7 × p⁷ × (0.8) ^10 - 7
= 0.000786432
The probability that exactly 7 belong to an ethnic minority is 0.000786432
