Answer:
19.63
Step-by-step explanation:
What is the sales tax of 5% on a purchase of $7.82?
A given line has the equation 10x+2y=-2. What is the equation , in slope intercept form, of the line that is parallel to the given line that passes through the point (0,12)
Answer:
y = -5x + 12
Step-by-step explanation:
Slope intercept form of a line is,
y = mx + c
Where, m is the slope of the line,
Here, the given equation of line,
10x+2y=-2,
2y = - 10x - 2
y = -5x - 1,
By comparing,
m = -5,
So, the slope of line 10x+2y=-2 is -5,
We know that the two parallel line have same slope,
Let the equation of the parallel line of the 10x+2y=-2 is,
y = -5x + c
According to the question,
It passes through the point (0,12),
That is (0, 12) must satisfy this line,
12 = -5(0) + c ⇒ c = 12,
Hence, the equation of the parallel line is,
y = -5x + 12
A state park is designed in a circular pattern as shown. A park ranger drives along the circular path from the ranger station to the nature center and then from the nature center to the petting zoo. How far does he drive to the nearest tenth of a mile?
A) 1.7 miles
B) 2.3 miles
C) 3.7 miles
D) 4.7 miles
Answer:B
Step-by-step explanation:
Given:Ranger Station to Nature Center = 90°Nature Center to petting zoo = 40°Petting Zoo to Tennis Court = 120°Tennis Court to Pool = 65°Pool to Ranger Station = 45°radius = 1 milearc length = 2πr angle/360°Ranger station to nature center.arc length = 2 * 3.14 * 1 mile * 90°/360°arc length = 2 * 3.14 * 1 mile * 0.25arc length = 1.57 milesNature center to Petting Zooarc length = 2 * 3.14 * 1 mile * 40°/360°arc length = 2 * 3.14 * 1 mile * 0.11arc length = 0.70 miles1.57 miles + 0.70 miles = 2.27 miles or 2.3 miles CHOICE B
On a drawing a triangle has sides that equal 4 cm, 5 cm, and 6 cm. If the scale of the drawing is 1 cm = 10 feet, find the sides of the original large triangle.
Answer:
A= 40 B=50 c=60
Step-by-step explanation:
Vanessa earns a base salary of \$400.00$400.00dollar sign, 400, point, 00 every week with an additional 5\%5%5, percent commission on everything she sells. Vanessa sold \$1650.00$1650.00dollar sign, 1650, point, 00 worth of items last week.
[tex]\\ \text{Given that the base salary of Vanessa is }\$400.00 \text{ every week}\\ \\ \text{And she gets an additional }5\% \text{ commission on everything she sells}.\\ \\ \text{Given that last week Vanessa sold }\$1650.00 \text{ worth of items,}\\ \text{so her commission last week was}\\ \\ =5\% \text{ of 1650}\\ \\ =0.05\times 1650\\ \\ =\$ 82.5\\ \\ \text{hence the total salary of Vanessa for last week}=400+82.5=\$482.5[/tex]
Hence the total salary of Vanessa last week was $482.5
The number of ways of selecting items where the order is not important, is known as a number of ________.
At a certain point in time, each dimension of a cube of ice is 30 cm and is decreasing at the rate of 2 cm/hr. How fast is the ice melting (losing volume)?
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Find the sum of the arithmetic sequence.
-4, -1, 2, 5, 8, 11, 14
A) 42
B) 35
C) -28
D) 17
Use the relationship between the angles in the figure to answer the question.
Which equation can be used to find the value of x? x = 52
x + 52 = 180
x + 52 = 90
52 + 38 = x
Answer: The answer is x= 52°
Step-by-step explanation: These are vertical angles so that means both sides would equal the same. One side is 52° So the other side would also be 52°.
Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off. The original price is $4.73. How much does she need to pay for the cereal?
Answer:
She needs to pay $4.38
Step-by-step explanation:
Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off.
The original price is $4.73. 35 cents off
35 cents can be converted into dollars when we divide by 100
35 divide by 100=0.35
to find the amount she need to pay, we subtract 0.35 from original price
Amount to pay=[tex]4.73-0.35=4.38[/tex]
find the sum of the interior angle measures of 18-gon
The sum of the interior angle measures of an 18-gon is calculated using the formula (n-2) imes 180 degrees, which equals 2880 degrees.
The sum of the interior angles of an n-gon (a polygon with n sides) can be found using the formula (n-2) imes 180 degrees. For an 18-gon, we can substitute 18 for n in the formula to calculate the sum of interior angles.
Sum of interior angles = (18-2) imes 180
Sum of interior angles = 16 imes 180
Sum of interior angles = 2880 degrees
Therefore, the sum of the interior angle measures of an 18-gon is 2880 degrees.
Jack decided to save 15% of his monthly allowance of $15.00. How much is he saving each month?
*show work*
Jack saving 2.25 $ each month
We have given that monthly allowance of jack is 15$
He decides to save 15% of his monthly allowances
We have to calculate the saving of each moth.
Therefore,
we have to find the 15% in decimal form,
What is the formula for finding the percentage in decimal form:
[tex]decimal form =\frac{x}{100}[/tex]
Where x is in %
Therefore,
15%=15/100=0.15
Jack want to save 0.15 from his monthly allowance of 15$
Therefore,
15(0.15)=2.25
Therefore,
Jack saving 2.25 $ each month.
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answer plz I reallllllly need it it is proportion
Find two positive numbers whose difference is 2828 and whose product is 39003900.
To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations and solve them using substitution or elimination.
Explanation:To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations. Let's assume the two numbers are x and y. From the given information, we have the following equations:
x - y = 2828
xy = 39003900
We can solve this system of equations by substitution or elimination. Let's use the substitution method:
From the first equation, we can express x as y + 2828. Substituting this into the second equation, we get (y + 2828)y = 39003900. Simplifying, we get y^2 + 2828y - 39003900 = 0.
Now we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula. Once we find the value of y, we can substitute it back into the first equation to solve for x. This will give us the two positive numbers.
A house on the market was valued at $314,000. After several years, the value increased by 17%. By how much did the house’s value increase in dollars? What is the current value of the house ?
Osvoldo has a goal of getting at least 30%, percent of his grams of carbohydrates each day from whole grains.
Today, he ate 220 grams of carbohydrates, and 5 grams were from whole grains.
Did Osvoldo meet his goal? Why?
yes/no Osvoldo ate (blank) grams of whole grains more/less than his goal.
explain please
No, Oswaldo did not meet his goal. He needed at least 66 grams of whole grains for his 220 grams of carbohydrates, but he only ate 55 grams, 11 grams less than required.
Let's check if Oswaldo met his goal of getting at least 30% of his carbohydrates from whole grains.
Calculate the percentage of whole grains :
Given:
- Total carbohydrates = 220 grams
- Whole grains = 55 grams
The percentage of carbohydrates from whole grains is calculated by:
[tex]\[ \text{Percentage} = \left( \frac{{\text{grams of whole grains}}}{{\text{total grams of carbohydrates}}} \right) \times 100. \][/tex]
Plugging in the values, we get:
[tex]\[ \left( \frac{{55}}{{220}} \right) \times 100 = 25\%. \][/tex]
Since the goal is at least 30%, but his actual percentage is only 25%, he did not meet his goal.
Calculate how much more whole grains he needed to meet his goal :
To get 30% of 220 grams, we need to calculate 30% of 220:
[tex]\[ 0.30 \times 220 = 66 \text{ grams}. \][/tex]
This means Oswaldo needed 66 grams of whole grains, but he only ate 55 grams.
The difference between what he needed and what he ate is:
[tex]\[ 66 - 55 = 11 \text{ grams}. \][/tex]
Thus, Oswaldo did not meet his goal, and he ate 11 grams less of whole grains than he needed to meet the goal.
The complete question is : Oswaldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains. Did Oswaldo meet his goal? Why? Yes No Oswaldo ate grams of whole grains more less than his goal.
Determine the decimal value of each signed binary number in the sign-magnitude form: (a) 10011001 (b) 01110100 (c) 10111111
Final answer:
To determine the decimal value of a signed binary number in sign-magnitude form, consider the sign and magnitude separately. (a) -102 (b) +116 (c) -64.
Explanation:
To determine the decimal value of a signed binary number in sign-magnitude form, you need to consider the sign and the magnitude separately.
(a) 10011001:
This number is negative in sign-magnitude form because the leftmost bit is 1. To find its magnitude, you invert the remaining bits (01100110) and convert it to decimal (102).
The final decimal value is -102.
(b) 01110100:
This number is positive in sign-magnitude form because the leftmost bit is 0. The magnitude is obtained by converting the bits (01110100) to decimal (116).
The final decimal value is +116.
(c) 10111111:
This number is negative in sign-magnitude form because the leftmost bit is 1. The magnitude is obtained by inverting the remaining bits (01000000) and converting it to decimal (64).
The final decimal value is -64.
(a) -25, (b) 116, (c) -63; sign bit denotes sign, remaining bits represent magnitude converted to decimal.
Let's go through each signed binary number in sign-magnitude form:
(a) 10011001:
Step 1: Determine the sign bit:
The leftmost bit, or the most significant bit (MSB), is the sign bit. In sign-magnitude representation, 1 denotes a negative number and 0 denotes a positive number. So, the sign bit here is 1, indicating a negative number.
Step 2: Convert the magnitude:
To find the magnitude, we ignore the sign bit and treat the remaining bits as a magnitude in binary form. So, the magnitude here is 0011001.
Step 3: Convert the magnitude to decimal:
The magnitude 0011001 in binary is equivalent to:
(1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 16 + 8 + 1 = 25
Step 4: Apply the sign:
Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10011001 in sign-magnitude form is -25.
(b) 01110100:
Step 1: Determine the sign bit:
The leftmost bit is 0, indicating a positive number.
Step 2: Convert the magnitude:
The magnitude here is 1110100.
Step 3: Convert the magnitude to decimal:
The magnitude 1110100 in binary is equivalent to:
(1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 64 + 32 + 16 + 4 = 116
Step 4: Apply the sign:
Since the sign bit is 0, indicating a positive number, the decimal value remains positive. Therefore, the decimal value of 01110100 in sign-magnitude form is 116.
(c) 10111111:
Step 1: Determine the sign bit:
The leftmost bit is 1, indicating a negative number.
Step 2: Convert the magnitude:
The magnitude here is 0111111.
Step 3: Convert the magnitude to decimal:
The magnitude 0111111 in binary is equivalent to:
(0 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) = 32 + 16 + 8 + 4 + 2 + 1 = 63
Step 4: Apply the sign:
Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10111111 in sign-magnitude form is -63.
So, the decimal values for each signed binary number in sign-magnitude form are:
(a) -25
(b) 116
(c) -63
Suppose consumers will purchase q units of a product at a price of StartFraction 200 Over q EndFraction plus 3 dollars per unit. What is the minimum number of units that must be sold in order that sales revenue be greater than $9000? The minimum number of units sold must be greater than nothing.
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3 sisters are each 2 years apart in age. The youngest sister is Emily, the middle sister is Samantha and the oldest sister is Lauren. Together their combined ages are 42. How old is each sister?
a. Define the variable(s).
b. Write an equation for this situation using one variable.
c. Solve the equation for the ages of the 3 sisters.
William bought Wiggit stock at 15.125 and sold it for 18. What was the percent of increase?
Which of the following is an unbiased question?
Which do you prefer, a nice, luxury Audi or a basic Ford?
Would you rather take a vacation to the mountains or to the ocean?
Which would you prefer, a chicken sandwich or a juicy, tasty burger?
Most people say they would prefer a new governor over the current one, what do you think?
it takes 45 minutes for 4 people to paint 5 walls. How many minutes does it take for 6 people to paint 4 walls?
In January, you deposit $16 in your checking account. Each month, you deposit $15 more than you did the month before. How much money do you deposit in October? A) $151 B) $166 C) $356 D) $835
The amount we deposited in the month of october is $151, option A is correct.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
We need to find the total amount deposited in 10 months, starting with $16 in January and increasing by $15 each month.
The first term is $16 and the common difference is $15.
The nth term can be found using the formula for the nth term of an arithmetic sequence:
an=a+(n-1)d
a=16, d=15
Now plug in n as 10, (10th month is october)
a₁₀=16+(10-1)15
=16+9(15)
=151
Hence, the amount we deposited in the month of october is $151, option A is correct.
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Which of the side lengths could form a triangle? A) 2 cm, 2 cm, 4 cm B) 3 cm, 5 cm, 10 cm C) 3 cm, 4 cm, 5 cm D) 4 cm, 8 cm, 15 cm Eliminate
Answer: The correct option is (C) 3 cm, 4 cm, 5 cm.
Step-by-step explanation: We are given to select the correct side lengths that could form a triangle.
We know that
the sum of the lengths of any two sides of a triangle is always greater than the third side.
That is, if a, b and c represents the lengths of three sides of a triangle, then we must have
[tex]a+b>c,~~b+c>a,~~c+a>b.[/tex]
Option (A) is
a = 2 cm, b = 2 cm, c = 4 cm.
We have
[tex]a+b=2+2=4=c~~~\Rightarrow a+b=c.[/tex]
Hence, this option is NOT correct.
Option (B) is
a = 3 cm, b = 5 cm, c = 10 cm.
We have
[tex]a+b=3+5=8<10=c~~~\Rightarrow a+b<c.[/tex]
So, this option is NOT correct.
Option (C) is
a = 3 cm, b = 4 cm, c = 5 cm.
We have
[tex]a+b=3+4=7>5=c~~~\Rightarrow a+b>c,\\\\b+c=4+5=9>3=a~~~\Rightarrow b+c>a,\\\\c+a=5+3=8>4=b~~~\Rightarrow c+a>b.[/tex]
So, this option is CORRECT.
Option (D) is
a = 4 cm, b = 8 cm, c = 15 cm.
We have
[tex]a+b=4+8=12<15=c~~~\Rightarrow a+b<c.[/tex]
So, this option is NOT correct.
Thus, (C) is the correct option.
Answer:
Option C.
Step-by-step explanation:
To form a triangle we should always remember that a triangle is possible when sum of two smaller sides of the triangle is greater than the largest side.
If smaller sides are a, b and largest side is c
Then a + b > c
Now we take each option given
Option A) 2 cm, 2 cm, 4 cm
2 + 2 = 4 which equal to the largest side so to form a triangle is not possible.
Option B) 3 cm, 5 cm, 10 cm
3 + 5 = 8 < 10 cm
Here sum of smaller sides is less than to the largest side so triangle will not be formed.
Option C. 3 cm, 4 cm, 5 cm
3 + 4 = 7 > 5 cm
Therefore triangle can be formed.
Option D) 4 cm, 8 cm, 15 cm
4 + 8 = 12 < 15 cm
so triangle can not be formed.
Option C is the correct option.
Fritz attended band practice for 5/6 hour then went home and practice for 2/5 as long as band practice how many minutes did he practice at home
Answer:
20 minutes
Step-by-step explanation:
5/6 x 2/5= 10/30
10/30 x 60 minutes = 600/30
simplify
600/30 = 20 minutes
Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?
The necklace charm shown has two parts, each shaped like a trapezoid with identical dimensions.
What is the total area, in square millimeters, of the charm?
Explain how to write thirteen divided by thirty-three as a divison expression AND as a fraction!
A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables. (a) Mrs. Roberts simplified this ratio to 2:6. Explain/show how you know she is incorrect. Can you tell where she might have made a mistake while simplifying?
A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables. (a) Mrs. Roberts simplified this ratio to 2:6. Explain/show how you know she is incorrect. Can you tell where she might have made a mistake while simplifying?
Solution:
So, A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables.
Ratio of dressing:vegetables=2:12.
Let us divide 2 and 12 by 2
Ratio of dressing: vegetables= [tex] \frac{2}{2} [/tex] : [tex] \frac{12}{2} [/tex]
So, finally we get ratio=1:6 and not 2:6. The mistake is in this step while simplifying.
So, Simplified Ratio of dressing:vegetables=1:6.
the stopping distance of an automobile is directly proportional to the square of its speed v. a car required 90 feet to stop when its speed was 70 miles per hour. find a mathematical model that gives the stopping distance d in terms of its speed v. Estimate the stopping distance if the brakes are applied when the car is traveling at 71 miles per hour.
The estimated stopping distance when the car is traveling at [tex]71\ miles\ per\ hour[/tex] is approximately [tex]{91.84}\ feet[/tex].
To find the mathematical model that relates the stopping distance [tex]\( d \)[/tex] to the speed [tex]\( v \)[/tex], given that stopping distance is directly proportional to the square of the speed, we can write:
[tex]\[ d = k v^2 \][/tex]
where [tex]\( k \)[/tex] is the proportionality constant.
Given that the car required [tex]90\ feet[/tex] to stop when its speed was[tex]70\ miles \ per\ hour[/tex], we can use this information to find [tex]\( k \)[/tex]
Convert the speed from miles per hour to feet per second (since [tex]1 \ mile = 5280 \ feet\ and\ 1\ hour = 3600 \ seconds[/tex]):
[tex]\[ 70 \text{ mph} = 70 \times \frac{5280}{3600} \text{ fps} = 102.67 \text{ fps} \][/tex]
Now, substitute [tex]\( v = 102.67 \) fps[/tex] and [tex]\( d = 90 \) feet[/tex] into the equation:
[tex]\[ 90 = k \times (102.67)^2 \][/tex]
Calculate [tex]\( (102.67)^2 \)[/tex]
[tex]\[ (102.67)^2 = 10545.84 \][/tex]
[tex]\[ 90 = k \times 10545.84 \][/tex]
Solve for [tex]\( k \)[/tex]
[tex]\[ k = \frac{90}{10545.84} = 0.00853 \][/tex]
Now, substitute [tex]\( k \)[/tex] back into the model:
[tex]\[ d = 0.00853 v^2 \][/tex]
Estimate the Stopping Distance at [tex]71 \ miles\ per\ hour[/tex]
Convert [tex]71 \ miles\ per\ hour[/tex] to feet per second:
[tex]\[ 71 \text{ mph} = 71 \times \frac{5280}{3600} \text{ fps} = 103.87 \text{ fps} \][/tex]
Now, calculate the stopping distance [tex]\( d \)[/tex] at this speed:
[tex]\[ d = 0.00853 \times (103.87)^2 \][/tex]
[tex]\[ d = 0.00853 \times 10781.14 \][/tex]
[tex]\[ d = 91.84 \][/tex]