NO LINKS!!
Write a mathematical model for the problem and solve it.
The sum of two consecutive natural numbers is 575. Find the numbers. (Enter your answers as a comma-separated list.)
Answer:
Step-by-step explanation:
To find the two consecutive natural numbers whose sum is 575, we can set up the following equation:
x + (x+1) = 575
where x and x+1 are the two consecutive natural numbers.
We can solve this equation by combining like terms:
2x + 1 = 575
Subtracting 1 from both sides, we get:
2x = 574
Dividing both sides by 2, we get:
x = 287
Therefore, the two consecutive natural numbers are 287 and 288. Our final answer is 287, 288.
Answer:
287,288
Step-by-step explanation:
Question
The sum of two consecutive natural numbers is 575. Find the numbers
soln
x +( x + 1) = 575
x + x + 1 = 575
2x + 1 = 575
2x = 575 – 1
2x = 574
\( \frac{2x}{2} = \frac{574}{2} \)
x = 287
since we got x as 287, lets solve(x+1)
by substituting
287 + 1 = 288
hence the consecutive numbers are 287,288
Check
287 + 288 = 575
we are correct.
i hope this helps
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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The human heart beats approximately 1.152x10^5 times per day. Approximately how many times does the heart beat per year?
The number of times does the heart beats per year is 4.2 x 10^7 times
How to determine the number of times does the heart beat per year?From the question, the given parameters are:
The human heart beats approximately 1.152x10^5 times per day
This means that
Daily heart beat = 1.152 x 10^5 times per day
There are 365 days in a year
So, the number of heart beats in a year is the product of the number of days in a year by the daily heart beats
So, we have
Yearly heart beat = Number of days in a year * Daily heart beat
Substitute the known values in the above equation
Yearly heart beat = 365 * 1.152 x 10^5 times
Evaluate the products
So, we have
Yearly heart beat = 420.48 x 10^5 times
Rewrite as
So, we have
Yearly heart beat = 4.2048 x 10^7 times
Approximate
Yearly heart beat = 4.2 x 10^7 times
Hence, the number of times does the heart beats per year is 4.2 x 10^7 times
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WILL MARK BRAINLIEST!!!
PLEASE HELP!!!
Solve for X.
Multiple choice!
Thank you!
Answer:
-8
Step-by-step explanation:
1) Total sum of all angles on a traingle is 180.
2) 65+40=105
3)180-105=75
4) -8+83=75
Answer:
x=-8 degree
Step-by-step explanation:
65 + 40 + x + 83 = 180 degree (sum of interior angles of a triangle)
188 + x = 180
x= 180 - 188
x=-8 degree
K
Each of the following three data sets represents the IQ scores of a random sample of adults. IQ
scores are known to have a mean and median of 100
105
105
111
105
111
102
106
91
99
99
109
99
109
111
115
112
Sample of Size 5
91
91
111
Sample of Size 12
888888 888
100
110
97
104
Sample of Size 30
91
111
113
113
108
113
108
91
118
110
Full data set o
101
109
101
109
91
97
95
CELES
m
For each data set, compute the mean and median
What is the mean of the sample of size 5?
(Type an integer or decimal rounded to one decimal place as needed
A 1.5 standard deviations above the mean IQ score is 122.5.
How do equations work?An expression that depicts the relationship between two or more numbers and variables is called an equation.
A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.
Giving the z score are:
z is calculated as (raw score - mean) / standard deviation.
with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:
1.5 = (x - 100)/15
x = 122.5
A 1.5 standard deviations above the mean IQ score is 122.5.
The Complete Question is IQ score.
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From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread. Which expession tells the weight of the flour left in the bag?
2-0.25
2-1.4
2-0.14
2-0.025
2.5-2
Brad works in the sales department for a furniture store. He earns a salary of $2,500 a month and a 3% commission if he meets his quota of $10,000 in sales for the month. If he doesn’t meet his quota but sells at least $5,000 worth of furniture, he gets 1.5% commission off of his sales. Brad sold $7,000 worth of furniture in May. What were his total earnings in May? ASAP PLEASE !!!!!!!!
Answer:
2605
Step-by-step explanation:
2500 + (7000*1.5%)
2500 + 105
2605
Can anyone please help?
Q: A baseball is hit into the air by the Blue Jays' batting coach.
It's height h, in meters, after t seconds is h = - 4.9t² + 27.44t + 0.584
(a) write the equation in vertex form by completing the square
b) How high off the ground was the ball when it was hit?
c) When does the ball reach it's maximum height? what is it's maximum height?
d) For how long is the ball in the air ? Round answer to 1 decimal place
The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.
The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:
h = -4.9(t² - 5.6t) + 0.584
Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:
h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584
Simplifying, we get:
h = -4.9((t - 2.8)² - 2.8²) + 0.584
Expanding further:
h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584
Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328
b) The ball's height when it was hit can be found by evaluating the equation at t = 0:
h = -4.9(0 - 2.8)² + 34.328
h = -4.9(-2.8)² + 4.328
h = -4.9(7.84) + 34.328
h ≈ 0.784 meters
To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.
The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:
0 = -4.9(t - 2.8)² + 34.328
4.9(t - 2.8)² = 34.328
(t - 2.8)² ≈ 7
t - 2.8 ≈ ±√7
t ≈ 2.8 ± √7
Since time cannot be negative in this context, we can ignore the negative value.
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A cyclist traveled 140 miles each day for 6 days if he cycled for 8 hours each day what was the unit ratio of miles per hour
Answer:
Step-by-step explanation:
the cyclist traveled 140 miles, each day, for 8 hours
in a day he traveled 140/8=17.5 miles per hour
Solve for
�
m. Express your answer in simplest radical form if necessary.
−
1
=
−1=
�
3
m
3
Answer:
To solve for m, we can cross-multiply the equation as follows:
−
1
3
=
1
�
3
−1
=
m
1
Multiplying both sides by m, we get:
−
�
3
=
1
−
3
m
=1
Multiplying both sides by -3, we get:
�
=
−
3
m=−3
Therefore, the solution is $m=-3$.
Step-by-step explanation:
PLS HELP MEEE
7y − 5 = 51
y =
Answer:
y = 8
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, add 5 to both sides of the equation:
7y - 5 = 51
7y - 5 (+5) = 51 (+5)
7y = 51 + 5
7y = 56
Next, divide 7 from both sides of the equation:
(7y)/7 = (56)/7
y = 56/7
y = 8
8 is your answer for y.
~
solve the system by substitution × = 6y -22x +5y =47
We have the following system:
\(\begin{gathered} x=6y-2\ldots(A) \\ 2x+5y=47\ldots(B) \end{gathered}\)Solving by substitution method.
If we substitute equation A into B, we get
\(2(6y-2)+5y=47\)which gives
\(12y-4+5y=47\)By combining similar terms, we have
\(\begin{gathered} 12y+5y-4=47 \\ 17y-4=47 \end{gathered}\)If we move -4 to the right hand side, we obtain
\(\begin{gathered} 17y=47+4 \\ 17y=51 \end{gathered}\)Then, if we move the coefficient of y to the right hand side, wehave
\(\begin{gathered} y=\frac{51}{17} \\ y=3 \end{gathered}\)Then, we can substitute this result into equation A, which gives
\(x=6(3)-2\)so, xi given by
\(\begin{gathered} x=18-2 \\ x=16 \end{gathered}\)Therefore, the answer is
\(\begin{gathered} x=16 \\ y=3 \end{gathered}\)Bailey is making festive cookie bags. She tried to split all her cookies evenly by putting 15 per bag, but the last bag had only 14 cookies. So, she tried putting 10 cookies per bag, but the last bag had only 9. Her mom brought 2 more cookies. Now, Bailey tries 9, then 8, cookies per bag, but she can’t do it. Finally, Bailey puts 7 cookies in each bag evenly! What is the least possible total number of cookies?
Answer:
Hi! The answer would be 21.
Step-by-step explanation:
First, we must add.
\(15 + 14 = 29\)
29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.
\(10 + 9 + 2 = 21 \)
21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.
Hope this helped!
B) What is the cost of making 35 items?
And c. The domain
The cost of making 35 items is 1100 and the domain is (-∞,∞)
The cost of making 35 items :
x = 35plug the value into the cost equation
C(35) = 10(35) + 800
C(35) = 350 + 800
C(35) = 1100
Hence, cost of making 35 items is 1100
The domain of the functionSince the value of X can be any real number, we can plug in any real number for x and get a real number output.
Hence, the domain = (-∞,∞)
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4) Visitors to an online store can enter a special code to receive a discount. The graph shows
the original price, , and sale price, y, of some items at the store.
What does the point at (60, 55) represent?
The point at (60, 55) means that an item with
an original price of $
?
has a sale price
of $ ?
Sale Price ($)
100
90
80
Online Store Prices
70
60
50
40
30
20
10
0
0 10 20 30 40 50 60 70 80 90 100
Original Price ($)
(30, 25)
(90, 85)
(60,55)
The point at (60, 55) represents an item with an original price of $60 that is now being sold at a sale price of $55.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
We are given that;
The point at (60, 55)
Now,
This means that customers who enter the special discount code can save $5 on this particular item.
In general, the point (x, y) on the graph represents an item with an original price of x dollars that is being sold at a sale price of y dollars. The graph is showing how the sale price of items changes as the original price increases.
Therefore, by the graph the answer will be $60 and $55.
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ATMOSPHERIC SCIENCE The troposphere extends from the Earth's surface to a height of 6-12 miles, dependin
on the location and the season. If a plane is flying at an altitude of 5.8 miles, and the troposphere is 8.6 miles deep in
that area, how much higher can the plane go without leaving the troposphere?
Answer:
2.8 Miles
Step-by-step explanation:
You subract 5.8 from 8.6 to get the answer.
If it takes 2men 11 days to dig 7 well, how many days should 7men dig 21well
7 men should be able to dig 21 wells in approximately 4.7 days.
How to determine the number of daysFrom the question, we have the following parameters that can be used in our computation:
If it takes 2men 11 days to dig 7 well, How many days should 7men dig 21wellWe can use the formula:
Number of days = (number of wells * number of days per well) / number of men.
So, we have
Number of days per well for 2 men:
11 days / 7 wells = 1.5714 days per well.
Using the above as a guide, we have the following:
the number of days for 7 men to dig 21 wells:
21 wells * 1.5714 days per well / 7 men = 4.7142days.
Hence, the number of days is 4.7 days.
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Which unit rate is the lowest price per ounce? (5 points)
Choice A: 21 ounces of raisins for $3.59
Choice B: 36 ounces of raisins for $4.79
Choice A
Choice B
The unit rates are equal.
The unit rates cannot be determined.
a
O
b
Od
Answer:
Choice B
Step-by-step explanation:
Choice A: 1 ounce of raisins for ~$0,17
Choice B: 1 ounce of raisins for ~$0,13
what is an expression to find the number of students in the art club when is it 3 more tan twice the number of students in the drama bluc.
The expression for the number of students in the art club would be 2x+3.
What is an expression ?
In mathematics, an expression is a combination of numbers, B operators, and/or functions, without an equals sign. It can be a single term, or a combination of terms separated by operators, such as addition, subtraction, multiplication, division, and exponentiation
Let the number of students in the drama club be x. Then, the expression for the number of students in the art club would be 2x+3, since it is 3 more than twice the number of students in the drama club.
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In a different field
number of goats: number of pigs = 13:4
Priya says.
"There are more than three times as many goats as pigs
Is she correct?
Tick one box
Yes
NO
Cannot tell
Show working to support your answer.
Answer:
yes
to determine if the statement is true, divide the ratio of goats by the ratio of pigs
13/4 = 3 1/4
there are 3 1/4 more goats as their are pigs
Step-by-step explanation:
Question 2(Multiple Choice Worth 2 points)
(Slope-Intercept Form MC)
The table shown represents a linear relationship.
x 0 1 3 4
y −8 −6 −2 0
Based on the table, what is the equation of the linear relationship in slope-intercept form?
y = 2x − 8
y = 2x + 8
y = −2x + 4
y = −2x − 4
The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.
To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.
By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).
Slope (m) = (change in y) / (change in x)
= (0 - (-8)) / (4 - 0)
= 8 / 4
= 2
Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.
Using the point (0, -8):
-8 = 2(0) + b
b = -8
Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.
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What is the length of one side of a square whose diagonal is 10 centimeters? Round to the nearest tenth, if necessary
A.12.6 cm
B.7.1 cm
C.40 cm
D.50.4 cm
HELP PLS ASAPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C; 5.32
Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!
write as a single power of 7.
7¹⁰ ÷ 7 =
Answer:
7^9
Step-by-step explanation:
when dividing you take away powers.
Answer:
7 to the power of 9
Step-by-step explanation:
7 by it self is 7 to the power of 1, and when you are dividing a power to subtract the power on top, so 10-1=9 and the answer is 7 to the power of 9 or 7^9
A survey conducted by the U.S. department of Labor found the 48 out of 500 heads of households were unemployed. Compute a 99% confidence interval for the proportion of unemployed heads of households in the population. Round to three decimal places. (make sure to type a zero in front of the decimal place ie. 0.1 vs .1 otherwise your answer will be marked incorrect) Lower limit
Answer:
99% Confidence interval is given as;
Lower Limit = 0.062
Upper Limit = 0.130
Step-by-step explanation:
Given the data in the question;
x = 48
n = 500
sample proportion p = x/n = 48/500 = 0.096
with 99% confidence
significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01
∝/2 = 0.01 / 2 = 0.005
Critical Z-value = \(Z_{\alpha /2\) = \(Z_{0.005\) = 2.576
Now,
Standard error of p : SE = √[ (p × ( 1 - p) / n ) ]
we substitute
SE = √[ (0.096 × ( 1 - 0.096) / 500 ) ]
SE = √[ (0.096 × 0.904) / 500 ]
SE = √[ 0.086784 / 500 ) ]
SE = 0.0131745
so
Margin of Error E = \(Z_{\alpha /2\) × SE
E = 2.576 × 0.0131745
E = 0.0339
Now 99% confidence interval will be
⇒ 0.096 ± 0.0339
⇒ (0.096 - 0.0339, 0.096 + 0.0339 )
⇒ ( 0.062, 0.130 )
Lower Limit = 0.062
Upper Limit = 0.130
A fair number cube with the numbers 1, 2, 3, 4, 5, and 6 is rolled. What is the
probability of getting a multiple of 3?
Your answer
Answer:
2/6
Step-by-step explanation:
There are only 2 multiples of 3, and there are only 6 possible outcomes.
Simplify: 2(4x - 6) - 8 + 10x
Answer:
Hi there!
The simplified version is:
18x-20
Step-by-step explanation:
2(4x-6) -8 +10x
First, multiply the 2 by the parentheses.
8x -12 -8 +10x
Next, combine like terms
18x -20
This is the simplified version!
Hope this helps
which type of statement has the form if a then B?
Answer:
A Conditional Statement
Answer:
Conditional would have that form.
What is the slope of the line passing through two points in the graph....
A random sample of adult men was asked if they would return the money if they found a wallet on the street. Of 143 men, 29 said they would. The true proportion of all adult men who would return the money is 18%. Which of the following do you expect would accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet?
Select one or more:
a. The mean of the sampling distribution will be equal to 0.18.
b. The mean of the sampling distribution will be equal to 0.2028.
c. The sampling distribution would be approximately standard normal.
d. The sampling distribution will be skewed right.
e. The sampling distribution will be skewed left.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Answer:
b. The mean of the sampling distribution will be equal to 0.2028.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Step-by-step explanation:
We use the Central Limit Theorem to solve this question.
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\).
The sample proportion being approximately normal means that option f. is correct.
Of 143 men, 29 said they would.
This means that \(p = \frac{29}{143} = 0.2028\)
This means that option b is correct.
g. The standard deviation of the sampling distribution will be 0.0336.
Lets find the standard deviation.
Sample of 143, so \(n = 143\)
\(s = \sqrt{\frac{0.2028*0.7972}{143}} = 0.0336\)
So option g. is correct.
The statements that accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet are;
B) The mean of the sampling distribution will be equal to 0.2028.
F) The sampling distribution will be approximately normal.
G) The standard deviation of the sampling distribution will be 0.0336.
Central Limit Theorem.
We are given the true proportion of all adult men who will return the money as; p = 18% = 0.18
Thus, the population mean = 0.18
Now, out of 143 men, 29 said they will return the money. Thus;
Sample mean = Sample proportion = 29/143 = 0.2028
The formula for the sampling standard deviation is;
s = √[p^(1 - p^)/n]
s = √[0.2028(1 - 0.2028)/143]
s = √0.001130574545
s = 0.0336
Looking at the options and comparing to the answers gotten above, only option B, F and G are correct.
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