A map is made of a park. The scale from the park to the map is 36 mi to 6 cm. The length of Great Oaks Trail is 4.5 cm on this map. The scale from the same park on a different map is 24 mi to 3 cm. The length of Salamander Trail is 3.5 cm on that map. What is the distance in miles of the Great Oaks Trail? What is the distance in miles of the Salamander Trail?
Answers
Answer:
27 miles
28 miles
Step-by-step explanation:
so, on the first map 6 cm on the map are 36 miles in real life.
the trail is 4.5 cm on the map.
therefore, we need to multiply the ratio 6/36 on top and bottom with the same factor (so that the ratio value remains unchanged).
which factor ? the factor that turns 6 into 4.5.
6×x = 4.5
x = 4.5/6
so, we have
6/36 × (4.5/6)/(4.5/6) = (6×4.5/6) / (36×4.5/6) =
= 4.5 / (6×4.5)
so, 4.5 cm on the map are 6×4.5 = 27 miles in real life.
in this case we could also make it faster :
the ratio 6/36 can be simplified to 1/6.
so, 1 cm on the map is 6 miles in real life.
now we see directly, that we only need to multiply this 1/6 ratio to and bottom by 4.5 (to get the 4.5 cm on the map) and we get
4.5 / (6×4.5) = 4.5 / 27
on the second map we have the ratio 3/24. that can Amado be simplified to 1/8.
we need 3.5 cm, so we need to multiply top and bottom by 3.5
1/8 × 3.5/3.5 = 3.5 / (8×3.5) = 3.5 / 28
so, that trail is 28 miles long.
for the general solution (if we cannot simplify the original ratio to 1/n) again, we need to turn 3 into 3.5.
what factor does this ?
3×x = 3.5
x = 3.5/3
so, we have
3/24 × (3.5/3)/(3.5/3) = (3×3.5/3) / (24×3.5/3) =
= 3.5 / (8×3.5)
therefore 3.5 cm on the map correlate to 8×3.5 = 28 miles in real life.
Related Questions
A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.
What is the sample size? Give only the number:
The margin of error for this data set is 2.5%. What is the 95% confidence interval for those who say they felt fully engaged with their mortgage provider (rounded to 1 decimal place)?
Answers
The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.
First, let's calculate the margin of error:
Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055
Next, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%
Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%
Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
To know more about Confidence interval visit: https://brainly.com/question/29680703
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answers
Answer:
The chi - square test can be \(\approx\) 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
\(Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}\)
For Monday:
\(Chi -square = \dfrac{(17 - 15 )^2}{15}\)
\(Chi -square = \dfrac{(2)^2}{15}\)
\(Chi - square = \dfrac{4}{15}\)
chi - square = 0.2666666667
For Tuesday :
\(Chi -square = \dfrac{(13- 15 )^2}{15}\)
\(Chi -square = \dfrac{(-2)^2}{15}\)
\(Chi - square = \dfrac{4}{15}\)
chi - square = 0.2666666667
For Wednesday :
\(Chi -square = \dfrac{(14- 15 )^2}{15}\)
\(Chi -square = \dfrac{(-1 )^2}{15}\)
\(Chi -square = \dfrac{(1 )}{15}\)
chi - square = 0.06666666667
For Thursday:
\(Chi -square = \dfrac{(16- 15 )^2}{15}\)
\(Chi -square = \dfrac{(1 )^2}{15}\)
\(Chi -square = \dfrac{(1 )}{15}\)
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be \(\approx\) 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
✔️z-=4z-2. Solve this problem. It should be the square root of z.
Answers
The equation is solved to give 16z² - z - 4 = 0
How to determine the valueNote that algebraic expressions are defined as expressions that are composed of terms, variables, coefficients, constants and also factors.
The expressions are also identified with mathematical operations, such as;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
√z= -4z - 2
Find the square of both sides, we get;
z = 16z² - 4
collect the like terms
16z² - z - 4
Equate to zero
16z² - z - 4 = 0
Learn more about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
Need help with this one will mark brainliest
Answers
Answer:
circle 3
Step-by-step explanation:
help pls :)) much appreciated
Answers
Answer:
9,-7 hope this helps :))))))))
April, May and June have
90
sweets between them. May has three-quarters of the number of sweets that June has.
April has two-thirds of the number of sweets that May has. How many sweets does June have?
help
Answers
Answer:
A
Step-by-step explanation:
The month of June has 40 sweets
Let the number of sweets in the month of June be P
Given that April, May and June collectively have 90 sweets
Given that May has three quarters of number of sweets as that of June
So we can write
\(\rm Number\; of \; sweets\; in \; May = \dfrac{3P}{4 } .......(1) \\\)
Similarly it is given that April has two third of sweets as that of May month and hence we can write
\(\rm Number\; of\; sweets \; in \; April = \dfrac{2}{3} \times \dfrac{3P}{4} = P/2 ......(2)\\\)
As the total number of sweets in April, May and June is 90
Let the number of sweets in May be "M" and in April be "A"
We can write the following equation and solve it further
\(\rm M + A + P = 90\\From \;equations \; (1) \; and \; (2) \\\)
\(\rm P + 3P/4 + P/2= 90\\\\2.25 \; P = 90\\P = 40\)
So we can conclude that the month of June has 40 sweets
For more information please refer to the link given below
https://brainly.com/question/1301963
simplify 2^3 ÷ 2^-3
leave your answer in the form 2^x, where x is an integer
these are the options for the answer
1
0
2^0
2^6
Answers
Answer:
\(2^{6}\)
Step-by-step explanation:
\(2^3 \div 2^{-3}\)
\(2^{3-(-3)}\)
\(2^{3+3}\)
\(2^{6}\)
QUESTION 4 PATTERNS, FUNCTIONS AND ALGEBRA 1. Given 6x³-8x³+2+9x7-4x a. How many terms are there in the polynomial? State the degree of the polynomial c. Determine the value of the polynomial if x=-1 b.
Answers
Answers:
a) There are 5 termsb) Degree = 7c) The value is -1==========================================
Explanation:
a) Each term is separated by a plus or a minus.b) The degree is equal to the largest exponent. This applies to single variable polynomials only.c) Replace each x with -1. Then use the order of operations PEMDAS to simplify. You should get -1 as the answer. Use a calculator to confirm. It is a coincidence that we have the same input and output. This will not always happen with any general polynomial function.Solve: x^2 – 16x + 63 < 0
Answers
Answer:
7 < x < 9
Step-by-step explanation:
x^2 – 16x + 63 < 0
this is a parabola that opens up.
The parabola will be < 0 for values between the roots.
to picture this see the graph below.
Factor
(x - 7)(x - 9) < 0
Roots
x = {7, 9}
solution
7 < x < 9
Please help me 7th grade math
Answers
Answer: 1/8
Step-by-step explanation: hoped this helped :))
A circle has a diameter of 18 inches. Which is the following is closet to the circumference of the circle?
Answers
Answer:25.13
Step-by-step explanation:
use the formulas
C=2πr
d=2r
On Monday, a local hamburger shop sold a combined total of 276 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answers
Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
To learn more about matrix visit:
https://brainly.com/question/29132693
#SPJ1
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the simplified value of the expression below?
-2.6 + 5.8
Answers
Answer:
3.2
Step-by-step explanation:
Answer:
3.2
Step-by-step explanation:
Ava answered 95/100 questions correctly on the test, and therefore believes to have earned a 95%. Is Ava correct?
Answers
Answer:
yes
Step-by-step explanation:
idk how to explain but, yes
Answer:
Yes, Ava is correct because percentages are always going to be out of one hundred.
In this case, there is 95%, which can also be put as .95 or 95 over 100 (95/100).
Hope this helps!
Please help. Math work.
Answers
Answer:
\( \frac{5}{6} \)
Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 along with an interest of $243. What was the annual interest rate? Round your answer to one decimal place.
Answers
9514 1404 393
Answer:
1.8%
Step-by-step explanation:
The effective rate can be found using the simple interest formula.
I = Prt . . . interest of principal P at annual rate r for t years
r = I/(Pt) . . . . solve for r
Using the given numbers, we have ...
r = 243/(4500·3) = 0.018 = 1.8%
The annual interest rate was 1.8%.
Which number has only two factors?
A
23
B
27
C
25
D
21
Answers
Answer:
a 23
Step-by-step explanation:
Mr. Bruce has some clay with a mass of 24 kilograms. If he puts the same amount of clay into 6 bags, how many grams of clay are in each bag? I NEED THE EXPLANATION
Answers
Answer:
4000grams in each bag
Step-by-step explanation:
Assume he put x amount of clay into each bag, he then put 6x into 6 bags.(since the question didn’t mention, I assume he put every clay he has into the bags)
6x=24kg
x=4kg
Since the question is asking for grams not kilograms:
4kg=4000g
If f(x)=x-9 and g(x)=-6x-3 which statement is true
Answers
Answer:
-1 is not in the domain of (f o g)(x)
Step-by-step explanation:
f(x) = sqrt(x - 9)
g(x) = -6x - 3
(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)
(f o g)(x) = sqrt(-6x - 3 - 9)
(f o g)(x) = sqrt(-6x - 12)
Let x = -1:
(f o g)(-1) = sqrt(-6(-1) - 12)
(f o g)(-1) = sqrt(6 - 12)
(f o g)(-1) = sqrt(-6)
Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).
Suppose P(x) = 3x 2−4x−7 is a quadratic function and we suspect that 8 3 is a zero of P(x). How can we confirm our suspicion?
Answers
P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.
What is quadratic equation and how to solve it ?
A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.
It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a).
We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.
To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).
P(8/3) = 3(8/3)^2 - 4(8/3) - 7
= 3(64/9) - 32/3 - 7
= 64/3 - 32/3 - 21/3
= 11/3
Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.
To know more about Quadratic equation visit:-
https://brainly.com/question/1214333
#SPJ1
Lyla goes out to dinner with her freinds where the subtotal is $78.41. A 6% tax and 15% tip is added to the subtotal. How much did she pay in total?
Answers
Tax = 0.06 and Tip = 0.15 basically making the percent into decimals we can add the two numbers to get a combined total of 0.21.
Now we can grab the total and multiply the two number, but we’ll add a 1 in-front of the decimal since we attempting to find the total after tax and tip is added.
So (78.41 x 1.21) = 94.8761 rounding up to the hundredth since we’re dealing with money so the answer is $94.88
PLEASE HELP Find the value of x.
X
15
12
Answers
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
Aaron was
making fruit punch for his study group. He used 6 cups
of orange juice, 11/2 cups of lemon juice and 3/4 cups
of pineapple juice. How many total cups of liquid did
Aaron mix altogether?
Answers
Answer:
12 1/4 cups
Step-by-step explanation:
11/2 = 5.5 cups
5.5 + 3/4=6.25 (which is basically,6 1/4)
6 1/4 + 6 = 12 1/4 cups
Find the area of each figure. (Or as much as u can)
Answers
9514 1404 393
Answer:
7. 91 m²
8. 56 in²
9. 105 in²
10. 135 m²
Step-by-step explanation:
The formula for the area of a triangle is ...
A = 1/2bh
where b is the base length, and h is the height perpendicular to the base.
The formula for the area of a trapezoid is ...
A= 1/2(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them. Note that this formula is virtually identical to the triangle formula, with the triangle 'b' being replaced by (b1+b2).
__
Fill in the numbers and do the arithmetic. The result is shown in the attachment. (We have used the triangle formula for all, with b1+b2 being used for 'b' to find the area of the trapezoids.)
7. A = 1/2(14 m)(13 m) = 91 m²
8. 56 in²
9. A = 1/2(14 +16 in)(7 in) = 105 in²
10. 135 m²
Label each as a function or not a function.
Answers
Answer:
Function, function
Step-by-step explanation:
Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions
. Ann ate 2 slices of a pizza and Teresa ate 3 slices of the pizza. The pizza had 8 slices. What is the difference in the amount of pizza that they ate written as a fraction?
Answers
A certain 12 - ounce soft drink
Answers
Answer:
Step-by-step explanation:
What
Answer: a certain 12 ounce drink contains about 10 teaspoons of sugar consumed. a certain 18 ounce drink contains about 15 grams of sugar consumed.
Step-by-step explanation: I hope this is what you were looking for.
HELP ME. I HATE MATH DUDE.
Answers
present ages of two children are 2 and 5 years the rspectively. After how long will the sum of their square ages be 45.
Answers
Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.
Calculating the duration to get the sum to 45Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.
Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;
let x represent the number of years from now when the sum of square of their respective age will be
45.(x + 2)² + (x + 5)² = 45
Expanding the brackets;
x² + 4x + 4 + x² + 10x + 25 = 45
2x² + 14x + 29 = 45
2x² + 14x + 29 - 45 = 0
2x² + 14x - 16 = 0
Solving the quadratic equation for x;
x = 1, x = -8
Taking the positive value, the value of x is 1
Learn more on age word problems here;
https://brainly.com/question/17043336
#SPJ1