a) The unit prices to determine the best buy are as follows:
6-ounce bottle = $0.2614-ounce bottle = $0.2420-ounce bottle = $0.28.b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.
What is the unit price?The unit price or cost is the cost for an item or a unit.
The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.
6 ounces 14 ounces 20 ounces
Total costs $1.56 $3.36 $5.60
Unit cost $0.26 $0.24 $0.28
($1.56/6) ($3.36/14) ($5.60/20)
Thus, buying a 14-ounce bottle of salad dressing is more economical than others.
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how to find the answer
x= 7; 4x + 8 ÷ 2 =
Answer: 18
unclear but appears its 18.
Step-by-step explanation:
Because x is 7; 4x+8/2 = 36.
but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.
a cone has a radius of 5.1 m and a slant height of 10.9 m. which would increase the cone's surface area more, doubling the radius or doubling the slant height?
A cone has a radius of 5.1 m and a slant height of 10.9 m. So the surface area of the cone is 87.3834 π m².
Determine the surface area of the coneThese are the specified parameters:
Radius (r) = 5.1 m
Cone height (h) = 10.9 m
Find the length of the cone painter's line (s)
s² = r² + h²
= 5.1² + 10.9²
= 26.01 + 118.81
= 144.82
s = √144.82
s = 12.034
Find the surface area of the cone
A = πr (r + s)
= π × 5,1 (5.1 + 12.034) m²
= 5.1 π (17.134) m²
= 87.3834 π m²
Which would increase the cone's surface area more is doubling the radius.
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if k is a positive two-digit integer, what is the tens digit of k ? (1) the sum of the tens digit of k and the units digit of k is 5. (2) the tens digit of k 6 is 3.
The tens digit of k when sum of its digits is 5 and tens digit of k + 6 is 3.
Let tens digit of k be x and units digit be y. Then
k = 10x + y
The sum of the tens digit of k and the units digit of k is 5, that is
x + y = 5
So possible combinations of (x, y) is (1, 4), (2, 3), (3, 2), (4, 1) and (5, 0).
The tens digit of k+6 is 3.
So x<=3.
14 + 6 = 20
23 + 6 = 29
32 + 6 = 38
So k is 32.
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Mark the givens in the diagram. Then copy the proof on paper, and fill in the blanks to complete the proof.
Given that
AR
∩
DC
= M, AD = RC and ∠A ≅ ∠R, prove that △MAD ≅ △MRC.
A
D
M
R
C
Statement1.
AD
= ____ Reason1. Given
2. ∠A ≅ ∠____ 2. Given
3. ∠AMD ≅ ∠____ 3. ________
4. △MAD≅ △____ 4. ________
The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC
How to complete the table?the table shows the statement and the reasons for the proves of congruency of the angles and triangles
The table appears as follows
sn Statement Reason
1 AD = RE Given
2 <A ≅<R Given
3 <AMD ≅<RMC Vertically opposite angles
4 ΔMAD≅ΔMRC Congruent by ASA or SSA
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The population of a city increases by 2.2% per year. If this year's population is 137,000, what will next year's population be, to the nearest individual?
The next year's population will be 140,014. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
For all real numbers, there are four fundamental mathematical operations that are:
1. The sum of the numbers is achieved through addition ('+').
2. Subtraction with the sign "-," which yields the numbers' differences.
3. Multiplication('×') when the result is the product of the numbers.
4. Division ('÷'), which yields the numbers' quotient.
We are given that the population of a city increases by 2.2% per year and this year's population is 137,000.
Let the population of next year be 'x'
So, we get
⇒137,000 + 137,000(2.2%) = x
⇒137,000 + 3014 = x
⇒140,014 = x
Hence, the next year's population will be 140,014.
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need help with this question...
Answer: C - The statement is false.
Step-by-step explanation: Rhombuses also have perpendicular diagonals.
How many vertices does this polyhedron have?
5
6
4
3
Answer:
4 I think
Step-by-step explanation:
A vertex is a point where two or more edges meet (i.e the sharp points of the figure).
A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.
Describe each x-intercept as "crosses" or "touches" the x-axis
If the graph only touches the x-axis at the x-intercept, then it is said to "touch" the x-axis. This indicates that the graph does not pass through the x-axis at the x-intercept, but rather just touches it.
What is the x-intercept?The x-intercept of a graph is the point at which the graph crosses the x-axis. It is also known as the abscissa. The x-coordinate of the x-intercept is the value where the graph intersects the x-axis.
The x-intercept of a graph is the point at which the graph crosses (or, in some cases, touches) the x-axis. A graph can have one or more x-intercepts. If the graph only crosses the x-axis once, then it has only one x-intercept. If the graph crosses the x-axis twice or more, then it has multiple x-intercepts. In either case, the x-intercepts can be described as either "crosses" or "touches" the x-axis.
If the graph crosses the x-axis at the x-intercept, then it is said to "cross" the x-axis. This indicates that the graph passes through the x-axis at the x-intercept.
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Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
Leslie and Joanne are in the same class. Their school day is 6 hours long. Joanne said that she was in school for 360 minutes. Leslie said she was in school for 320 minutes. Complete the table below to see who is correct.
Answer:
.
Step-by-step explanation:
Find the volume of the given prism. Question 3 options: A) 3,568 in3 B) 1,920 in3 C) 6,336 in3 D) 1,784 in3
The area of the given prism is equal to 1,920 in³.
What is a rectangular prism?
A rectangular prism is simply a three-dimensional solid shape which with six faces that are rectangles.
We have given,
length l = 8 in.
width w = 12 in,
height h = 20 in.
The volume of a prism is defined as the total space occupied by the three-dimensional object.
The volume of a rectangular prism is given by A = l * w * h,
where 'l' is the length of the prism, 'w' is the width, and 'h' is the height.
so, A = 8 * 12 * 20 = 1,920 in³.
A = 1,920 in³.
Therefore, the area of the given prism is equal to 1,920 in³.
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The table below shows all of the possible outcomes for rolling two six-sided number cubes.
What is the probability of rolling an even number first and an odd number second?
The probability of getting 1st even and second odd is 9/36 = 1/4
What is Probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.
Number of outcomes with 1st even and second odd is 9
Total number of outcomes = 36
So, the probability of getting 1st even and second odd is 9/36 = 1/4
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How do you write a function from a table of values?
A function can be obtained from the table provided with the values of x and y in the form of a y=mx+b equation.
The above equation can be solved by plotting the graph or from table itself and after calculating its y-intercept, the value of y in the form of y= mx+ b can be obtained. Suppose the table has values of x and y as follows:
x: 0 1 2 3
y: 2 4 6 8
However, it can be seen that when x=0, y= 2, so the y-intercept i.e. the value of y obtained at x=0 is 2. And the slope can be calculated as:
m=[tex]\frac{change in y}{ change in x}[/tex]
m= [tex]\frac{4-2}{1-0}[/tex]
m=2
So the function can be written as y=2x+2
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Grayson is working two summer jobs, making $18 per hour lifeguarding and making $10 per hour clearing tables. In a given week, he can work a maximum of 14 total hours and must earn no less than $180. Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables. If xx represents the number of hours lifeguarding and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities that models this situation is given as follows:
x ≥ 0.y ≥ 3.x + y ≤ 14.18x + 10y ≥ 180.x ≤ 10.One possible solution is given as follows:
(9,4).
Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.
How to model the system of inequalities?The variables for the system of inequalities in this problem are given as follows:
Variable x: number of hours lifeguarding.Variable y: number of hours clearing tables.The number of hours cannot be negative, hence the first two restrictions are given as follows:
x ≥ 0.y ≥ 0.He can work a maximum of 14 total hours, hence:
x + y ≤ 14.
He must earn no less than $180, hence, considering the rates for each job, we have that:
18x + 10y ≥ 180.
Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:
x ≤ 10.y ≥ 3.The shaded region represents all possible solutions for the system of inequalities.
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1 Comparing discounts Mai has two coupons for pants. Coupon A: Coupon B: 40% off of $51 pants $18 rebate on $51 pants Choose the coupon that gives the lower price. Then fill in the blank with the correct value. Coupon A gives the lower price. The price with coupon A is less than the price with coupon B. Coupon B gives the lower price. The price with coupon B is $less than the price with coupon A.
Answer:
Coupon A
Step-by-step explanation:
Coupon A takes 40% off
51 x .40= $20.40
Coupon B only gives a rebate for $18
Coupon A is $2.40 less than the price with coupon B
Select all the expressions that are equivalent to 9/7x−3/4.
The expressions that are equivalent to 9/7x−3/4 are:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
What is the linear equation?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
All of the following expressions are equivalent to 9/7x−3/4:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
When you multiply or divide both the numerator and denominator of a fraction by the same non-zero number, the fraction remains equivalent.
Hence, the expressions that equivalent to 9/7x−3/4 are:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
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the length of a rectangle is 3 more than twice its width. the total area of the rectangle is 54 square units. what is the width and length of the rectangle?
The width and length of the rectangle is 4.5ft and 12ft.
Width of a rectangle = b = x ft.
Length of a rectangle = l = (2x+3) ft.
Area of the rectangle = l×b = 54 sq.ft.
= x (2x + 3) = 54
= 2x² + 3x = 54
(2x-9)(x+6) = 0
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
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How many dimes and quarters equal $6.55?
Answer: 25q and 3d
Step-by-step explanation:
23 dimes and 17 quarters equal $6.55.
To find the number of dimes and quarters which equals $6.55, we can use the following method:
Let D = number of dimes
Let Q = number of quarters
40 coins ==> D + Q = 40 ==> D = 40 - Q
$6.55 total ==> 10*D + 25*Q = 655
After the value for D is substituted in the second equation,
10*(40 - Q) + 25*Q = 655
400 - 10*Q + 25*Q = 655
15*Q = 255
Q = 17
i.e., D = 40 - 17 = 23
Check: 23 dimes = $2.30
17 quarters = $4.25
Total = $6.55
Therefore, 23 dimes and 17 quarters equal $6.55.
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22. In your day-to-day routines, you use measurement to cook or do home renovations such as adding new tile floors. How do you imagine that you will use measurement in your future career?
The measurement that you can use in your future career depends on the exact career and there are many more options.
Depending on the exact career but measurements are plentiful in the healthcare business. First, you'll most likely deal with weight and height... since that's part of most healthcare consultations. Then, if you deal with medication, you'll use grams, milligrams, milliliters, and liters all the time. depending if the medication is in solid or liquid form.
Even as a nutritionist, you'll deal with grams and such for portion sizes. There are countless ways you'll use mathematics and measurements in the healthcare sector.
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Line AD is parallel to line HE, what is the value of x?
Answer: [tex]110^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.
Your friend is confused about types of debts. Which of the following would most likely help his financial portfolio by adding an appreciating asset?boat loancar loanmortgagenone of the above
In his financial portfolio by adding an appreciating asset is mortgage
The term portfolio is defined as a collection of a wide range of assets that are owned by investors.
Here we have said collection of financial assets may also be valuables ranging from gold, stocks, funds, derivatives, property, cash equivalents, bonds, etc.
Here we have given that Your friend is confused about types of debts.
as per the definition of portfolio, here we must also understand the concept of financial portfolio,
The term financial portfolio is defined as a collection of investments and holdings like stocks, bonds, mutual funds, commodities, crypto, cash, and cash equivalents.
Hence the correct option is (c).
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Classify each polynomial based on its degree and number of terms. Drag each description to the correct location. Each description can be used more than once. binomialtrinomialmonomial8th degreefour termsquinticcubicquarticquarticquadratic
Answer:
Step-by-step explanation:
Quadratic: binomial
Cubic: trinomial
Quartic: four terms
Quintic: five terms
8th degree: six terms
The product of a number, x, and 0.28 is 13.44. Which equation matches this statement?
Answer Selection
0.28 divided x = 13.44
0.28x = 13.44
13.44x = 0.28
x divided 13.44 = 0.28
Answer: The correct equation that matches the statement "The product of a number, x, and 0.28 is 13.44" is:
0.28x = 13.44
This equation states that when a number x is multiplied by 0.28, the result is 13.44.
Step-by-step explanation:
a pair of dice are tossed. what is the probability that doubles are rolled, given that the sum on the two dice is less than 7?
Answer:
To solve this problem, we will use the following steps:
Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).
Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.
Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.
Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.
Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.
Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.
Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.
Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.
5/18 = 0.278
Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 8.7
Step-by-step explanation:
The remaining interior angle is [tex]95^{\circ}[/tex].
[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]
A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 20 inches by 14 inches, what size square must be cut if the volume of the box is to be 288 cubic inches
The square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.
What is square?Square is a two-dimensional shape with four equal sides and four right angles. It is one of the most common shapes in geometry. Squares have many practical uses, such as in forming grids, creating patterns, and making tiling. Squares are also used in art and architecture, as well as in construction, mathematics, and science.
To solve this problem, we will use the formula for the volume of a rectangular box, V = lwh. We can substitute the given values to solve for x. First, we will find the length and width of the box after the square corners are cut out:
Length = 20 - 2x
Width = 14 - 2x
Now, substituting these values into the volume formula, we get:
288 = (20 - 2x)(14 - 2x)h
Expanding and simplifying, we get:
288 = 280 - 56x + 4x^2
Subtracting 280 from both sides, we get:
8 = -56x + 4x^2
Solving for x, we get:
4x^2 - 56x + 8 = 0
Using the quadratic equation, we get x = 2.4 or x = 0.4
Since x must represent a length, we can discard the negative solution, x = 0.4. Therefore, the square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.
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Select the correct answer from each drop-down menu. Look at the tables of values below. Data Set 1 Data Set 2 x y -2 6 0 6 1 4 3 2 5 0 x y 1 -2 3 2 3 0 5 8 7 5 Data set is not a function, while data set is a function. To turn the data set that is not a function into a function, the point can be changed so that the x-value is not equal to . Reset Submit
Data set 2 is not a function, while data set 1 is a function. To turn the data set that is not a function into a function, the point (3,0) can be changed so the x-value is not equal to 1, 3, 5 or 7.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
In input-output format, the points in these relations are given as follows:
(x,y).
Hence a data-set will represent a function if each value of x is mapped to a single value of y.
This means that data-set 1 represents a function, while data-set 2 does not, as the value of x = 3 is mapped to both y = 2 and y = 0.
The data-set 2 will represent a function if one of the x-coordinates of 3 is changed to another x-coordinate, that is also different of the other x-coordinates of the table.
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6.2÷(2x+1)= 7/3÷4 What is the answer?
Answer: x= 337/70 or 4 57/70
Step-by-step explanation:
taotao wants to buy a bracelet. the bracelets have different beads on them, arranged in a circle. if she can choose the colors and placement of the beads, and the beads come in orange, white, and black, how many possible bracelets can she buy?
Think of a bracelet made of five different coloured beads. Be sure to account for flipping and rotating. Check to see whether your solution is right by applying the same logic to a bracelet with four beads of four different colours.
For what is circle renowned?Properties. The form with the biggest area for a given perimeter is a circle (see Isoperimetric inequality). The circle has excellent spherical shape around the centre for all angles and every line thru the centre generates a path of reflection symmetry.
My response is: There are (n-1)!/2 potential bracelets for n different colours, as in our example. Therefore, there are 4!/2=12 various bracelets that might be made for n=5.
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What is the Inverse of 2(x-5)^2
The inverse function of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Let, y = 2(x - 5)².
y/2 = (x - 5)².
Solving for 'x'.
[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].
[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]
Now, We have to interchange the positions of x and y.
[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
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A researcher made the following graph showing the number of hours per day that people spend on the computer versus the number of pounds that they overweight. predict the number of pounds overweight someone would be if they spent 8 hours per day using a computer
PLS I NEED HELP!!
Answer:
Step-by-step explanation:
Unfortunately, without more information, it is not possible to accurately predict the number of pounds someone would be overweight if they spent 8 hours per day using a computer. The graph provided does not provide enough data to make an accurate prediction. It is possible, however, to make an educated guess based on the graph. Looking at the graph, it appears that someone who spends 8 hours per day on the computer would likely be somewhere between 20 and 40 pounds overweight.