the cost of ketchup is $3.53 & mustard is $0.63 .
Step-by-step explanation:
Here we have , Brianna bought 3 bottles of ketchup and 2 bottles of mustard for $11.85. Logan bought 3 bottles of ketchup and 5 bottles of mustard for $13.73. We need to find the cost of each. Let's find out :
Let cost of ketchup be x and mustard be y than ,
Brianna bought 3 bottles of ketchup and 2 bottles of mustard for $11.85
We have following equation ,
⇒ [tex]3x+2y=11.85[/tex] ..........(1)
Logan bought 3 bottles of ketchup and 5 bottles of mustard for $13.73
We have following equation ,
⇒ [tex]3x+5y=13.73[/tex] ........(2)
Now , (2) - (1) , i.e.
⇒ [tex]3x+5y-(3x+2y)= 13.73-11.85[/tex]
⇒ [tex]3y= 1.88[/tex]
⇒ [tex]y=0.627[/tex]
Putting value of y in (1) :
⇒ [tex]3x+2(0.627)=11.85[/tex]
⇒ [tex]3x=11.85-1.254[/tex]
⇒ [tex]x=3.532[/tex]
Therefore , the cost of ketchup is $3.53 & mustard is $0.63 .
The cost of each bottle of ketchup is $3.532 and cost of each mustard is $0.626
Explanation:
Given:
3 bottles of ketchup + 2 bottles of mustard = $11.85
3 bottles of ketchup + 5 bottles of mustard = $13.73
Cost of each = ?
Let x be the cost of each bottle of ketchup
Let y be the cost of each bottle of mustard
According to the question:
3x + 2y = $11.85
3x + 5y = $13.73
Substituting both the equation, we get:
3x + 2y = $11.85
3x + 5y = $13.73
________________
-3y = -1.88
y = $0.626
Substituting the value of y = $0.626 in equation 1
3x + 2(0.626) = $11.85
3x + 1.252 = $11.85
3x = 10.598
x = $3.532
Therefore, cost of each bottle of ketchup is $3.532 and cost of each mustard is $0.626
Y= 4.6, 13.9, 21.6, ????
Option B: 13.9 is the value of y
Explanation:
Given triangle is a right angled triangle.
The legs of the triangle are 8 and y.
The hypotenuse of the triangle is x.
And the angle opposite to y is 60°
We need to determine the value of y.
Let us find the value of y using the tangent formula.
The formula for tan is given by
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Since, we know that [tex]\theta = 60^{\circ[/tex] , [tex]opp=y[/tex] and [tex]adj=8[/tex]
Substituting these values in the formula, we get,
[tex]tan \ 60^{\circ}=\frac{y}{8}[/tex]
Multiplying both sides by 8, we have,
[tex]8\times tan \ 60^{\circ}=y[/tex]
Substituting the value of [tex]\tan 60^{\circ}[/tex] , we get,
[tex]8\times 1.732=y[/tex]
Simplifying, we have,
[tex]13.856=y[/tex]
Rounding off, we get,
[tex]13.9=y[/tex]
Thus, the value of y is 13.9
Hence, Option B is the correct answer.
Which function has the given properties below? The domain is the set of all real numbers. One x-intercept is (StartFraction pi over 2 EndFraction, 0 EndFraction). The maximum value is 3. The y-intercept is (0, –3).
Answer:
y = -3cosx
Step-by-step explanation:
Let me rewrite your question:
One x-intercept is ( pi/2 , 0) so we know that it is a trigonometric function such as cosine that has x-intercept (pi/2,0). The maximum value is 3, it means the amplitude must be 3: y = 3 cos x The y-intercept is (0,-3), means when x =0, y will equal to negative 3 (-3) then it is the function y = -3cosx,So y = -3cosx is the function has the given properties
The solution to an inequality is 5≤x<9. What is the smallest value of x that will make the original inequality true?
Answer:
5
Step-by-step explanation:
It is given that the solution to an inequality is
[tex]5\leq x<9[/tex]
It means the original inequality is true for any values of x which is greater than or equal to 5 and less than 9.
We need to find the smallest value of x that will make the original inequality true.
[tex]5\leq x\text{ and }x<9[/tex]
Therefore, smallest value of x is 5 that will make the original inequality true.
Seventy-five percent of what number is 37.5?
Answer: 37.5 is 5% of 57.6923077
Step-by-step explanation:
The number where 75% of it equals 37.5 is 50.
To find the number, we can set up an equation based on the given information: 75% of a certain number is equal to 37.5. Mathematically, this can be represented as:
0.75x = 37.5
To isolate x, we can divide both sides of the equation by 0.75:
x = 37.5 / 0.75
Evaluating the division:
x = 50
Therefore, the number we are looking for is 50.
The equation 0.75x = 37.5 states that 75% (or 0.75 as a decimal) of a certain number x is equal to 37.5. By dividing both sides of the equation by 0.75, we "undo" the multiplication and solve for x. Dividing 37.5 by 0.75 gives us the value of 50.
To check our solution, we can substitute x = 50 back into the original equation:
0.75 x 50 = 37.5
37.5 = 37.5
The equation holds true, confirming that 50 is indeed the number where 75% of it equals 37.5.
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(-w^3 + 8w^2 – 3w) + (-8w^2 + w + 3) =
8 more than a number p is 17 equation
Answer:
17=p+8
Step-by-step explanation:
Start by setting the equation equal to 17 on either the right or left side. Now, on the opposite side of the equation read out what the question is saying.
"8 more than a number (p)" the variable would be p, and 8 more than p is 17. Now that you have that in mind, write 17 is equal to p plus 8.
17=p+8
If the question asks you to solve this equation for p, subtract 8 from both sides to get 9 for p.
I hope this is easy to understand.
0) Rodney had $60 to spend on sports equipment. After buying 6 footballs, he had $7.50. How
much did each football cost?
Answer:
$8.75
Step-by-step explanation:
He had $60 to spend on sports equipment.
He bought 6 footballs and was left with $7.50
First get the amount used in buying all the footballs
That’s
$60 - $7.50 = $52.5
He bought the 6 balls for $52.5
Therefore, amout paid for each football will be amount spent in buying the footballs divided by number of footballs bought
That’s
$52.5/6 = $8.75
Each football cost $8.75
The harmonic mean of two numbers, a and b, equals 2/ 1/a +1/b. As you vary the length of a violin or guitar string, its pitch changes. If a full-length string is 1 unit long, then many lengths that are simple fractions
produce pitches that harmonize, or sound pleasing together. The harmonic mean relates two lengths that produce harmonious sounds. Find the harmonic mean for the string lengths of 1 and 1/2
Answer:
2/3
Step-by-step explanation:
2 / (1/a + 1/b)
2 / (1/1 + 1/(½))
2 / (1 + 2)
2/3
The harmonic mean is [tex]2\div 3[/tex]
Calculation of the harmonic mean:Since the string lengths of 1 and 1/2
So,
[tex]= 2 \div (1/a + 1/b)\\\\= 2 \div (1/1 + 1/(1\div 2))\\\\= 2 \div (1 + 2) \\\\= 2\div 3[/tex]
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A square is inscribed in a circle. If the area of the square is 49 square units, what is the radius of the circle?
a
√2/7 unit
b
(7√2)/2 units
c
7√2units
d
14√2 units
Answer:
B
Step-by-step explanation:
If it is inscribed in the circle that means all four corners of the square are touching the circle
so therefore the diagonal of the square is the diameter of the circle
the side lengths of the square as you know is 7 units ([tex]\sqrt{49[/tex]) the length of the diagonal is [tex]7\sqrt{2}[/tex] heres how I know
If you cut the square in half through the centre diagonally you will get a right isosceles triangle, using the pythagorus theorum
[tex]7^2+7^2=C^2\\49+49=C^2\\98=C^2\\\sqrt{98}=C\\C=7\sqrt{x}[/tex]
Now we have the diameter
it's just half of that, so the answer is B
For a square inscribed in a circle, the length of the diagonal of the square equals the diameter of the circle. Given the area of the square is 49 units, the length of a side is 7 units, and thus the diagonal (or diameter of the circle) is 7√2 units. Therefore, the radius of the circle is half of the diameter, which is (7√2)/2 units.
Explanation:In this question, we need to determine the radius of a circle in which a square is inscribed. The square has an area of 49 square units. In a square inscribed in a circle, the diameter of the circle is equal to the diagonal of the square. Thus, if 'a' is the length of a side of the square, the length of the diagonal, which is the diameter of the circle, is 'a√2'.
Given that the area of the square is 49 units, 'a^2=49' or 'a=7' units. Therefore, 'a√2' = '7√2' units. As this is the diameter, the radius of the circle is half of the diameter thus, it equals '(7√2)/2' units. Which means option b '(7√2)/2' units is the correct answer.
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what is the perimeter of this tile 6in 2in
Answer:
16 inches
Step-by-step explanation:
The perimeter of the tile is 16 inches. The perimeter of a shape is the total length of all of its sides added together.
In this case, the tile has two sides that are 6 inches long and two sides that are 2 inches long.
To find the perimeter, we can add all of the side lengths together:
Perimeter = 6 inches + 6 inches + 2 inches + 2 inches
Perimeter = 16 inches
Therefore, the perimeter of the tile is 16 inches.
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please help a fellow strugglin student out
look at the system of equations below.
y = -2x + 3
4x - 3y = 11
what is the solution to the system? show your work.
Answer:
x=2, y= -1
Step-by-step explanation:
Please see attached picture for full solution.
Each wheel of Gia's bicycle is 24 inches in diameter. Gia rides her bike 1,884 feet. To
the nearest whole number, how many times does her front bicycle wheel turn all the
way around?
The front wheel turns around approximately 300 times.
To determine how many times Gia's bicycle wheel turns around during her 1,884 feet ride, we need to calculate the circumference of the wheel and then divide the total distance traveled by the circumference.
The diameter of the wheel is 24 inches. To find the circumference (C), we use the formula C = pi x d, where d is the diameter, and (pi) is approximately 3.14159.
C = 3.14159 x 24 inches = 75.39816 inches.
Next, we need to convert the distance Gia rode her bike from feet to inches because the circumference is in inches. There are 12 inches in a foot, so
1,884 feet x 12 inches/foot = 22,608 inches.
Now we divide the total distance traveled in inches by the circumference of the wheel to find out how many full revolutions there are:
22,608 inches / 75.39816 inches/revolution ≈ 300 revolutions.
To the nearest whole number, Gia's front bicycle wheel turns all the way around 300 times.
Decrease 620 by 10%
Answer:
682
Step-by-step explanation:
620, percentage decreased by - 10% (percent) of its value = 682
Scientists are studying a group of living cells under a microscope. They write down notes about the size, shape, and color of the cells as well as other traits.
Which best describes this type of investigation?
comparative, because the scientists will be making observations in order to form a hypothesis
comparative, because the scientists are measuring dependent and independent variables
descriptive, because the scientists are using independent variables to test a hypothesis
descriptive, because the scientists are writing down observations but not making comparisons
Answer: answer is D, descriptive, because the scientists are writing down observations but not making comparisons
Step-by-step explanation:
According to the question, the scientists were making individual notes on their observation about shape, colour, size and other characteristics of the living cells. We do not have enough information to show that they were making comparisons.
I hope this helps.
Answer:
anwser D
Step-by-step explanation:
discreptive because scientist are writing dow explanations
Help me find the area pls
Answer: 49m
Step-by-step explanation:
4m, 1m and 2m add up to 7m on the right side. so, L x W= 7x7 which is 49
JL has coordinates J(-6, 1) and L(-4,3).
Find the coordinates of the midpoint.
Answer:
The coordinates of the mid-point of JL are (-5 , 2)
Step-by-step explanation:
If point (x , y) is the mid-point of a segment whose end-points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then [tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ JL is a segment
∵ The coordinates of J are (-6 , 1)
∴ [tex]x_{1}[/tex] = -6 and [tex]y_{1}[/tex] = 1
∵ The coordinates of L are (-4 , 3)
∴ [tex]x_{2}[/tex] = -4 and [tex]y_{2}[/tex] = 3
Lets use the rule above to find the mid-point of JL
∵ [tex]x=\frac{-6+-4}{2}=\frac{-10}{2}[/tex]
∴ x = -5
∴ The x-coordinate of the mid-point is -5
∵ [tex]y=\frac{1+3}{2}=\frac{4}{2}[/tex]
∴ y = 2
∴ The y-coordinate of the mid-point is 2
∴ The coordinates of the mid-point of JL are (-5 , 2)
Final answer:
The coordinates of the midpoint of the segment with endpoints J(-6, 1) and L(-4,3) are obtained by averaging the x and y coordinates of the endpoints, resulting in (-5, 2).
Explanation:
To find the coordinates of the midpoint of a segment with endpoints J(-6, 1) and L(-4,3), you use the midpoint formula which is ((x1 + x2)/2, (y1 + y2)/2). In this case, x1 is -6, x2 is -4, y1 is 1, and y2 is 3. Plugging these into the formula, we get the midpoint coordinates ((-6 - 4)/2, (1 + 3)/2) which simplifies to (-5, 2). Therefore, the midpoint of JL is at the coordinates (-5, 2).
johnny has 24 soap bottles he shares half of all the soap bottles with his friends how many soap bottles does johnny have left
Answer: Johnny will have 12 soap bottles left
If f(x) = 7 + 4x and g(x)= 7x, what is the value of (f/g)(5)
The value of [tex](\frac{f}{g})(5)[/tex] is [tex]\frac{27}{35}[/tex]
Explanation:
Given that [tex]f(x)=7+4x[/tex] and [tex]g(x)=7x[/tex]
The value of [tex](\frac{f}{g})(5)[/tex]:
The value of [tex](\frac{f}{g})(5)[/tex] can be determined by substituting x = 5 in the functions f(x) and g(x) and then dividing the terms, we get, the value of [tex](\frac{f}{g})(5)[/tex]
Thus, we have,
[tex](\frac{f}{g})(5)=\frac{f(5)}{g(5)}[/tex]
Substituting the value of x = 5 in the functions f(x) and g(x), we get,
[tex](\frac{f}{g})(5)=\frac{7+4(5)}{7(5)}[/tex]
Simplifying the terms, we have,
[tex](\frac{f}{g})(5)=\frac{7+20}{35}[/tex]
Adding the terms in numerator, we have,
[tex](\frac{f}{g})(5)=\frac{27}{35}[/tex]
Thus, the value of [tex](\frac{f}{g})(5)[/tex] is [tex]\frac{27}{35}[/tex]
you deposit $1600 in an account. The annual interest rate is 5% for 3 years. How much
interest will you earn on the money?
Answer: $240
Step-by-step explanation:
Simple interest= Principal x Rate x Time
Where P= 1600, R= 5% = 0.05, T=3
= 1600 x 0.05 x 3
$240
I ONLY HAVE A LITTLE TIME ANS NEED HELP!!!!! can someone explain this to me
Answer:
x = 92
Step-by-step explanation:
[tex]\frac{x}{46} =\frac{78}{39}[/tex]
I did big side over small side, proportions.
Cross Multiply.
39x = 3,588
divide by 39x
x = 92
Answer:
92
Step-by-step explanation:
These triangles are similar because they share a common angle and two pairs of sides in the same ratio.
Sides of the bigger triangle are double of those of the smaller triangle
46+46 = 92
A class contains 13 girls and 15 boys.
What is the ratio of boys to girls?
How many students are there in all?
What fraction of the students are girls?
The ratio of boys to girls will be 15 : 13.
There are 28 students in all.
The fraction of the students are girls will be 13/28.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
Given that;
A class contains 13 girls and 15 boys.
Now,
Since, A class contains 13 girls and 15 boys.
Hence, Number of total students = 13 + 15
= 28
So, The ratio of boys to girls = Number of boys : Number of girls
= 15 : 13
Hence, Number of total students = 13 + 15
= 28
And, The fraction of the students are girls is;
= Number of girls / Number of students
= 13 / 28
Thus, The ratio of boys to girls = 15 : 13.
Total number of students = 28
And, The fraction of the students are girls = 13/28.
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The product of 2 and the sum of 5 is 8
Answer:26
Step-by-step explanation:
2x(8+5)
2x13=26
at a farm 15 of the 20 chicken are hens what percent of the chicken in the farms hens
Answer: 75 percent of the chicken are hens.
If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.
Ratio of areas of similar triangles is 9 : 25.
Solution:
Given data:
Ratio of sides of two similar triangles = 3 : 5
To find the ratio of areas of the triangles:
We know that,
In two triangles are similar, then the ratio of their area is equal to the square of the ratio of their sides.
[tex]$\text{Ratio of areas} = \frac{\text{Area of triangle 1}}{\text{Area of triangle 2} }[/tex]
[tex]$=\left(\frac{3}{5}\right) ^2[/tex]
[tex]$=\frac{9}{25}[/tex]
Ratio of areas of similar triangles is 9 : 25.
Answer:
16
:
81
Explanation:
Scale factor for the sides of these triangles.
k
=
4
9
.
Therefore the ratio of area will be:
k
2
=
Area Triangle A
Area triangle B
k
2
=
(
4
9
)
2
=
16
81
A tea vendor gives samples of tea in cone shaped cups. The cups have a diameter of 4 inches and a height of 5 inches. If there are about 0.55 fluid onces in one cubic inch, how many fluid ounces of tea will one sample hold? Round to the nearest tenth
One sample cup will hold 11.51 ounces of fluid.
Step-by-step explanation:
Diameter of cone shaped cup = 4 inches
Radius = [tex]\frac{Diameter}{2}=\frac{4}{2}=2\ inches[/tex]
Height of cup = 5 inches
Volume of cone = [tex]\pi r^2 \frac{h}{3}[/tex]
Putting values
Volume of cone = [tex]3.14*(2)^2*\frac{5}{3}\\[/tex]
Volume of cone = [tex]3.14*4*\frac{5}{3}=\frac{62.8}{3}[/tex]
Volume of cone = 20.93 inches cubed
Amount of fluid in one cubic inch = 0.55 ounces
Amount of fluid in 20.93 cubic inches = 0.55*20.93 = 11.51 ounces
One sample cup will hold 11.51 ounces of fluid.
Which of the following terms have a GCF of ? Select two options
Answer:
the answers are A) 18p^3r and D) 54p^3
Good luck! :)
Answer:
A) 18p³r
D) 54p³
Step-by-step explanation:
The term 6p³ multiplies into (or goes into) both 18p³r and 54p³.
Line segment CD is 5 inches long. if line segment CD is dilated to form line segment C'D' with a scale factor of 0.6, what is the length of line segment C'D'.
Answer:
3 inches
Step-by-step explanation:
5 inches * 0.6 scale factor = 3 inches
Answer:
3 inches
Step-by-step explanation:
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.
Weights of eggs: 95% confidence; n=53, /x =1.34 oz, standard deviation = 0.58 oz
A.) (0 pts) 0.13 oz
B.) (0 pts) 0.02 oz
C.) (1 pts) 0.16 oz
D.) (0 pts) 0.36 oz
Answer: option c
Step-by-step explanation:
margin of error = critical value × s/√n
Where s = sample standard deviation = 0.58, n = 53
The critical value = 1.96 ( this is the critical value for a two test test corresponding to a level of significance of 5%)
By substituting the parameters, we have that
Margin of error = 1.96×0.58/√53
Margin of error = 1.96 × 0.0796
Margin of error = 0.156 ~ 0.16
Answer:
0.16 oz
Step-by-step explanation:
I think i know but I probably have it wrong, will give Brainliest
Answer:
164 square feet
164 ft^2
Step-by-step explanation:
Base: 10 × 4 = 40 (×2 = 80)
Front/back face: 10 × 3 = 30 (×2 = 60)
Left/right face: 3 × 4 = 12 (×2 = 24)
Add: 80 + 60 + 24 = 164
Damon buys lumber worth $562. He gets 20% contractor discount. The sales tax is 6%. his credit card gives him 2% off. How much does he pay?
Answer:
$467.05
Step-by-step explanation:
The price is $562
First, 20% off of that:
562 - 20% of 562 = 562 - 0.2(562) = $449.60
Second, he has to pay 6% tax on this amount, so:
6% = 6/100 = 0.06
449.60 + 0.06*449.60 = $476.58
He won't be paying this amount, because paying through credit card will give him 2% discount on this, so:
476.58 - 0.02(476.58) = $467.05
Final Price: $467.05