Answer: Composite
Step-by-step explanation: To see if 35 is a prime number or a composite number, let's first start by finding the factors of 35.
To find the factors of 35, begin by dividing 35 by 1 which gives us 35. This means that 1 and 35 are factors.
Next, since 35 is not divisible by 2, 3, or 4, we divided 35 by 5 which gives us 7. This means that 5 and 7 are factors.
Next, since 35 is not divisible by 6, we divide 35 by 7 which gives us 5. Notice that 7 and 5 are repeat factors and once we hit repeat factors, this means that all other factors we try will repeat.
Therefore, the factors of 35 are 1, 5, 7, and 35.
Since 35 has more than two factors, it's called a composite number.
mary purchased 3 1/2 pounds of bananas. If the loaf of banana bread requires 3/4 pounds of bananas, how many loaves of banana bread can she make with the bananas.
the product of x and y, in three different ways; the product of the sum and the difference of x and y, using parentheses
What's 9376 rounded to?
Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
Find all solutions of the equation 2sin2x−cosx=1 in the interval [0,2π), what is x?
The following list shows the items and prices for a restaurant order. Calculate the total amount if there is 7.5% tax and the customer leaves a 15% gratuity.
1 appetizer: $8.99
2 entrees: $14.99 each
1 entree: $12.99
3 drinks: $1.99 each
a. $70.96
b. $71.62
c. $75.31
d. $75.97
The first thing we are going to do to find the total cost of the meal before tax:
Total cost before tax = $8.99 + 2($14.99) + $12.99 + 3($1.99)
Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97
Total cost before tax = $57.93
Regarding the 15% gratuity, remember that the unofficial rule for tipping at restaurants is to tip according to the actual value of the meal and not the tax, so we calculate the value of the tip first, and then we add it to the total at the end of our calculations.
Tip = 15%($57.93) = $8.69
Now, lets calculate the tax
Tax = 7.5%($57.93) = $4.34
Finally, we can calculate the total cost of the meal
Total cost = cost before tax + tip + tax
Total cost = $57.93 + $8.69 + $4.34 = $70.96
We can conclude that the correct answer is a. $70.96
Answer:
$70.96
Step-by-step explanation:
Cost of 1 appetizer = $8.99
Cost of 1 entrees= $14.99
Cost of 2 entrees= [tex]14.99 \times 2 = 29.98[/tex]
Cost of 1 entree: $12.99
Cost of 3 drinks = 1.99 \times 3 =5.97
Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97
Total cost before tax = $57.93
there is 7.5% tax
So, tax =[tex]7.5 \% \times 57.93 = \frac{7.5}{100} \times 57.93 =4.34[/tex]
The customer leaves a 15% gratuity.
Gratuity=[tex]15 \% \times 57.93 = \frac{15}{100} \times 57.93 =8.69[/tex]
So, Total cost including tax and gratuity = $57.93 + $8.69 + $4.34 = $70.96
So, Option A is true
Linda has 4 2/3 yards of material . She is making baby clothes for the bazzaar. Each dress patterns requries 1/16 yards of material. How many complete dresses will she be able to make from the material she has?
compute the following linear combinations. 4(-2,3)-2(6,-7) ...?
Answer:
Step-by-step explanation:
alright lets get started.
the linear combination is given by :
[tex]4(-2,3)-2(6,-7)[/tex]
foiling 4 and 2 into the parenthesis
[tex](4*-2, 4*3)+(-2*6,-2*-7)[/tex]
[tex](-8, 12)+(-12,14)[/tex]
Combinig x and y terms together
[tex](-8-12, 12+14)[/tex]
[tex](-20,26)[/tex] : answer
Hope it will help. :)
in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
The odds in favor of winning $5 or more at the carnival are 3 to 10.
To determine the odds in favor of winning $5 or more at the carnival, we need to consider the number of tickets that win $5 or more and the total number of tickets.
Identify the tickets that win $5 or more: Yellow tickets win $5 and Blue tickets win $10.
Count the number of these tickets:
Yellow tickets: 25
Blue tickets: 5
Total tickets that win $5 or more:
25 + 5 = 30
Total number of tickets:
100 + 25 + 5 = 130
Odds in favor of winning $5 or more is the ratio of favorable outcomes to unfavorable outcomes:
Winning tickets: 30
Non-winning tickets:
130 - 30 = 100
Simplified odds:
30 to 100 = 3 to 10
Therefore, the odds in favor of winning $5 or more are 3 to 10.
The odds in favor of winning $5 or more in a carnival drawing are 3 : 10. So, the correct option is (B).
To determine the odds in favor of winning $5 or more in a carnival drawing, observe the number of tickets for each prize and calculate the favorable outcomes.
Here are the ticket counts:
Green ticket ($1): 100 ticketsYellow ticket ($5): 25 ticketsBlue ticket ($10): 5 ticketsFirst, calculate the total number of tickets:⇒ 100 (green) + 25 (yellow) + 5 (blue) = 130 tickets
Next, calculate the number of tickets that win $5 or more:⇒ 25 (yellow) + 5 (blue) = 30 tickets
The remaining tickets are the losing tickets or those winning less than $5 (green):⇒ 130 (total) - 30 = 100 tickets
Therefore, the odds in favor of winning $5 or more are 30:100, which simplifies to 3:10. This converts to the following odds as a ratio:
So, the correct option is (B) 3:10.
Complete question:
In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5 and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:1
B. 3:10
C. 2:1
D. 1:3
Suppose the function shown below was expressed in standard form, y=ax^2+bx+c. What is the value of a? the graph shows a parabola facing downward with a vertex of (1,4) and the x intercepts are (3,0) and (-1,0) with a y intercept of (0,3)
...?
This is the graph they are referring to
Write the equation of the line that passes through (7,-4) and (-1,2) in slope-intercept form
83.3333 rounded to nearest tenth of a percent ...?
what is the largest perfect square of 45? ...?
The largest perfect square less than or equal to 45 is 36, which is the square of 6. Squaring numbers less than 7 shows that 36 is the perfect square closest to, but not exceeding 45.
Explanation:The largest perfect square that is less than or equal to 45 is the result of the greatest integer squared that does not exceed 45. To find this, you would look for the highest whole number whose square is less than or equal to 45. The numbers less than 45 are 1, 2, 3, ..., and so on. Squaring these: 12=1, 22=4, 32=9, 42=16, 52=25, 62=36. The next number, 7, squared is 49, which is greater than 45. Therefore, 62=36 is the largest perfect square less than or equal to 45. This concept is essential when simplifying square roots or in problems dealing with areas of squares.What is the radical form of each of the given expressions? 4 1/7 AND 4 7/2 AND 7 1/4 AND 7 1/2 I WILL UPVOTE
Simplify √550
A 5√22
B 10√55
C 5√11
D 25√5
Answer:
A) 5√22
Step-by-step explanation:
I took the K12 quiz and it was right
The simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The number in radical sign is 550 ie.
= √550
The factors of the 550 can be written as:
550 = 5x5x2x11
= √(5x5x2x11)
= 5√(2x11)
= 5√22
Thus, the simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.
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Given the mapping diagram, DAYS (month), below, DAYS (July) = _____
Answer:
July has 31 days.
Step-by-step explanation:
The diagram shows that april has 30 days along with June, while May and July have 31 days.
Solve. e^(4x) + 5e^(2x) - 24 = 0.
Prove: the midpoint of the hypotenuse of a right triangle is equidistant from three vertices
From the picture attached,
Coordinates of point A → (0, 0)
Coordinates of point M → [tex](\frac{a}{2}, \frac{b}{2} )[/tex]
Coordinates of point A → (0, b)
Coordinates of point A → (a, 0)
Since, we have to prove that midpoint (M) of the hypotenuse BC is equidistant from all three vertices A, B and C,
AM = BM = CM
Use the expression for the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AM = [tex]\sqrt{(\frac{a}{2}-0 )^2+(\frac{b}{2}-0)^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2} )^2}[/tex]
BM = [tex]\sqrt{(a-\frac{a}{2} )^2+(\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
CM = [tex]\sqrt{(0-\frac{a}{2} )^2+(b-\frac{b}{2})^2}[/tex]
= [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
Therefore, AM = BM = CM = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]
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YES, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices -
AM = CM = BM.
We have a right - angled triangle → ΔABC.
We have to prove that midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
What is Right Angled Triangle?A right angled triangle is a triangle with one of the angles as 90 degrees.
According to the question -
Consider the hypotenuse BC. The mid - point of BC has the coordinates as -
M([tex]\frac{a}{2} , \frac{b}{2}[/tex]).
Now -
Length AM →
AM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length CM →
CM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2} - b) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Length BM →
BM = [tex]\sqrt{(\frac{a}{2} -a) ^{2} + (\frac{b}{2} ) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]
Therefore -
AM = CM = BM
Hence, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices.
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10 POINTS!
Solve.
6 – 3x = 4(3 – x) – 6
A.
0
B.
–6
C.
all real numbers
D.
6
I am a quadrilateral with two sets of parallel sides, all my sides have the same length, who i am?
A family has two cars. the first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. during one particular week, the two cars went a combined total of 775 miles, for a total gas consumption of 35 gallons. how many gallons were consumed by each of the two cars that week?
The range of which function includes -4?
A. y=sqrt(x)-5
B. y=sqrt(x)+5
C. y=sqrt(x+5)
D. y=sqrt(x-5)
Answer: The correct answer is A.
Step-by-step explanation:
Range is defined as the set of 'y' values for which the function is defined.
The graph of [tex]y=\sqrt{x}[/tex] passes through the origin and lies in the first quadrant and in the shape of half parabola. The image is attached below.
The alteration in the 'x' term will transform the graph in the x-direction. In order to find the range we will consider the y-values only. So, we can neglect option C and D.
When we add some constant 'C' in the function, then the graph will shift upward by C-units.
When we subtract some constant 'C' in the function, then the graph will shift downward by C-units.
Therefore, the graph of [tex]y=\sqrt{x}-5[/tex] starts with the point (0,-5) and hence, the graph will lie above this point. The image of the graph is attached below.
As, the range of the function is [tex]y\in {-5,\infty}[/tex], it means that -4 is also included in this range.
Hence, the correct option is A.
The correct option where the range includes -4 is y = sqrt(x) - 5. Other options do not produce negative values in their ranges. Hence, Option A is the correct answer.
To determine which function's range includes -4, we will analyze each option:
Option A: y = sqrt(x) - 5Based on the above analysis, the correct answer is Option A: y = sqrt(x) - 5.
find the square root of 1.69? show work ...?
The value of the square root of the number 1.69 would be 1.3.
Used the concept of the square root of a number that states that,
The square root of a number is the number that, when multiplied by itself, gives the original number.
Given that the number is,
The square root of 1.69.
Now simplify the number as
The square root of 1.69.
It can be written as,
√1.69
√(1.3)²
= 1.3
Therefore, √1.69 = 1.3
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Nellie is buying bird seed to put in her bird feeders. She uses about 10 pounds of bird seed each week, but has room to store any extra that she purchases.The bird seed comes in 3 different sizes as given below: 3.5 pounds for $2.52 7.5 pounds for $5.40 11 pounds for $7.92 Nellie is trying to be a smart shopper and get the best deal on the bird seed. Which size bag of bird seed should Nellie buy?
All the bird seed bags Nellie is considering have the same cost per pound ($0.72). She should choose based on her weekly usage and storage preference. Any size will be cost-effective.
To determine the best deal on bird seed, Nellie needs to calculate the unit price for each option. The unit price is the price per pound of bird seed.
For the 3.5-pound bag:
[tex]\[ \text{Unit price} = \frac{\$2.52}{3.5 \text{ pounds}} \approx \$0.72/\text{pound} \]\\For the 7.5-pound bag:\[ \text{Unit price} = \frac{\$5.40}{7.5 \text{ pounds}} = \$0.72/\text{pound} \]For the 11-pound bag:\[ \text{Unit price} = \frac{\$7.92}{11 \text{ pounds}} \approx \$0.72/\text{pound} \][/tex]
Since all three options have the same unit price of approximately $0.72 per pound, Nellie should choose the size that offers her the most pounds of bird seed for the best value, as he has anyway room for storing extra purchase. Here, can choose to buy any of them.
WILL UPVOTE!
Factor the expression.
x^2 -12x +36 =
marathon runner runs26.2 miles at the pace of 6.2 minute per mile round off answer to the nearest minute how long will it take to run marathon
If the length of one of the legs of a right triangle is 10 and the length of the other leg is 24 what is the length of the hypotenuse
Answer:
the hypotenuse is probably 26
Step-by-step explanation:
Write the ratio 7/8 :14 as a fraction in its simplest form
The length of a rectangle is 5 inches less than 3 times the width. The perimeter of the rectangle is 14 inches. Find the length and width of the rectangle.
I did this: Length 3x-5; width 3x Then I did guess and check and came up with X=2 solving the problem with a perimeter of 14. But, the answer is supposed to be length 4inches, width 3inches.
Please explain what I did wrong. I know the answer but not how to get it.
write a fraction that is equivalent to 7/10 = _ /_
$10,000 is invested at two different rates. $4,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.