Answer:
decimal form is limited of 3 numbers after the point only.
so it will be 1.45
I hope I help you in this ans and tq.
The weights of a pack of chewing gum for a certain brand have a mean of 47. 1 grams and a standard deviation of 2. 4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3. 11?
The weight of a randomly selected pack of gum that has a z-score of 3.11, is 54.6 grams. So, the right option is D.
A Z-score can be used to calculate how much the data deviates from the mean. It shows how frequently the data is either above or below the mean. According to the formula,
Z = (X - μ)/σ
where, Z is the Z-score, X is the data point, μ is the mean and σ is the standard variable.
Z = 3.11, σ = 2.4, μ = 47.1
Z = (X - μ)/σ
Now putting the value
3.11 = (X - 47.1)/2.4
Multiply by 2.4 on both side
X - 47.1 = 3.11 X 2.4
X - 47.1 = 7.464
Add 47.1 on both side, we get
X = 54.564 grams
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The complete question is:
The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3.11?
39.6 grams
44.7 grams
49.5 grams
54.6 grams
The number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6. 5 and a standard
deviation of 0. 58. What is the probability that a random sample of 40 adults would have a mean of at least 7
marshmallows?
approximately 0
0. 1943
0. 2934
0. 5367
The probability that a random sample of 40 adults would have a mean of at least 7 marshmallows is 0.1943
We know that the formula for the z-score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To find: the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows.
This is nothing but the p-value of Z when X = 7
Here the number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6. 5 and a standard deviation of 0. 58
So, mean μ = 6.5
standard deviation σ = 0.58
Also, n = 40,
x = 7,
By central limit theorem,
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{7-6.5}{0.58}\\\\z=\frac{0.5}{0.58}\\\\z = 0.86[/tex]
z = 0.86 has p value 0.1943
Thus, the required probability is 0.1943
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Bottles Glue Glitter
1 3.8 1.9
This means,
1 bottle = 3.8 oz of glue and 1.9 oz of glitter
Now,
1 bottle = 3.8 oz of glue
Multiply 4 on both sides.
4 bottle = 4 x 3.8 oz
4 bottle = 15.2 oz
1 bottle = 1.9 oz of glitter
Multiply 4 on both sides.
4 bottle = 7.6 oz
Thus,
15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
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MATHHHHH PLEASEEEEEEE
Answer:
halfway between 862350 and 862360
(x^3+5x^2-24x)/(x+8) Synthetic Division
The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is x² - 3x.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is given below:
(x³ + 5x² -24x) / (x + 8)
The divisor is -8
The coefficients are:
1 5 -24
Using synthetic division
the first coefficient is 1
the second coefficient = 1 * (-8) + 5
the second coefficient = -3
the third coefficient = -3 * (-8) + (-24)
the third coefficient = 0
Therefore, the solution = 1(x³/x) -3(x²/x) + 0(x/x)
The solution = x² - 3x
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A number N divides each of 17 and 30 with the same remainder in each case. What is the largest value N can have?
The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30
What is remainder in a division operation?The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.
The remainder following the division of 17 and 30 by the number N are the same.
Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;
17/N = Q + R/17
30/N = b·Q + R/17
30/N - 17/N = 13/N
The substitution property indicates that we get the following equation;
30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q
30/N - 17/N = b·Q - Q
13/N = b·Q - Q = (b - 1)·Q
13/N = (b - 1)·Q
The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13
13 is a prime number, therefore, the factors of 13 are 13 and N
Therefore, the possible values of N are 13 and 1
The largest value N can have is therefore, 13
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estimate 3.71 x 0.296 by rounding each number to the place of its leftmost nonzero digit.
The estimate of the product expression is 0.12
How to estimate the expressionFrom the question, we have the following parameters that can be used in our computation:
3.71 * 0.296
From the question, the numbers are to be rounded to the place of its leftmost nonzero digit.
So, when the numbers are rounded, we have
4 * 0.3
Evaluate the product
This gives
0.12
Hence, the solution is 0.12
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determine whether the pairs of triangles are congruent.
Quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , find EF .
We are given that quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , then the side EF= -34.
What is a quadrilateral?
A quadrilateral is a four-sided polygon, or a shape with four straight sides. It is a type of closed, two-dimensional shape. The four sides of a quadrilateral can be of equal or varying lengths and angles. Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, and trapezoids.
Since quadrilateral EFGH is a rectangle, the opposite sides are congruent and parallel.
Therefore, if EF = 4x - 6 and HG = x + 3, then HG=EF
so, x+3=4x-6
then, x=-9
Therefore, EF=4x-6=4(-9)-6= -34
Hence, EF= -34
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Is the following is considered a LINEAR table. True or False.
The following is considered a LINEAR table is True .
What is mean by LINEAR table?By observing how X and Y vary, you may determine whether a table is linear. A table is linear if Y rises at a steady pace as X increases by 1. Finding the initial difference allows you to determine the constant rate.Look for a consistent rate of change to establish if the function is linear or nonlinear.The rate of change between any two rows in the table may be calculated.Pick another set of rows and figure out how much they have changed at this point.Both change rates are the same.There are several instances of linear equations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.To learn more about LINEAR table refer to:
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What is the factored form of this expression?
-9x^3 - 12x^2 - x4
The factored form of the expression -9x^³ - 12x² - 4x is given as follows:
A. -x(3x + 2)².
How to simplify the expression?The expression for this problem is defined as follows:
-9x^³ - 12x² - 4x.
The exponents of the expression are given as follows:
3, 2 and 1.
The lowest exponent is of:
1.
Simplifying the lowest exponent, the expression is given as follows:
-x(9x² + 12x + 4)
The inner expression can be obtained with the square of the sum, as follows:
9x² + 12x + 4 = (3x + 2)².
Meaning that the simplified expression is of:
-x(3x + 2)².
Which is option A.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The diameter of a tire is 2. 5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit.
a. Find the circumference of the tire.
b. About how many times will the tire have to rotate to travel 1 mile? (1 mile = 5,280 ft)
a) The circumference of the tire is 7.85 ft
b) About 673 times the tire will have to rotate to travel 1 mile.
The diameter of a tire is 2. 5 ft.
Let r represents the radius of the tire.
r = diameter/2
r = 2.5 / 2
r = 1.25 ft
a) the circumference of the tire:
We know that the formula for the circumference of circle:
C = 2πr
So, the circumference of the tire would be,
C = 2 × π × r
C = 2 × π × 1.25
C = 7.85 ft
b) Let the tire will have to rotate n times in order to travel 1 mile.
We know that 1 mile = 5,280 ft
So, n = 5280 / 7.85
n = 672.6
n ≈ 673
Thus, the tire will have to rotate 673 times in order to travel 1 mile.
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at what intercepts is the graph constant
Answer:
for any two points in the interval, a change in x results in a zero change in f(x)
Step-by-step explanation:
What is the reverse of multiplied by 146 
The Multiplicative Inverse of postive 146 is 0.00684932.
What is Multiplicative Inverse?
The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.
When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.
The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.
Given number for the multiplicative inverse is 146;
so, If the Multiplicative Inverse of 146 is x
then , the problem can be written as a function as follows:
146(x) = 1
Thus, to get the answer, we divide 1 by 146 like this:
1 / 146 = 0.00684932
Therefore,the Multiplicative Inverse of postive 146 is 0.00684932.
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Circle the representation that has the less steep slope.
Pls help me with 3 and 4
The line of linear equation y = 8x - 48 is much steeper than the line of linear equation y = -x - 4-.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[16 - 32]/[8 - 10]
(-16)/(-2)
8
So, the slope point is obtained as m = 8.
The equation becomes - y = 8x + b
To find the value of b substitute the values of x and y in the equation -
32 = 8(10) + b
32 = 80 + b
b = 32 - 80
b = -48
So, the value for b is -48.
Now, the equation becomes -
y = 8x - 48
A graph has been plotted for the equation.
Similarly, the points for a line is given as (-6,2) and (-9,5).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[5 - 2]/[-9 - (-6)]
(3)/(-9 + 6)
3/-3
-1
So, the slope point is obtained as m = -1.
The equation becomes - y = -x + b
To find the value of b substitute the values of x and y in the equation -
2 = -(-6) + b
2 = 6 + b
b = 2 - 6
b = -4
So, the value for b is -4.
Now, the equation becomes -
y = -x - 4
A graph has been plotted for the equation.
It is known that the larger the slope the steeper the line.
In the graph also it can be seen that the graph of line y = 8x - 48 is much steeper.
Therefore, the slope of line y = 8x - 48 is more steeper.
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One apple costs S0.55 at the grocery store. Customers receive one free apple for every 8 apples that they buy. Anna paid a total of $8.80 for her apples. How many apples did Anna receive?
Answer:
She was given 1 free apple and paid for 15 apples.
Step-by-step explanation:
0.55x2=1.1
1.1x8=8.8
8.8/.55=16
16-1=15
And you know she paid for 15 apples and got 1 free.
Eric bought a canoe for $333.75. The sales tax was 5.25%. What was his total cost?
jenny got a box of 15 stickers . then she used 5 on a thank you card what fraction of the box did she used
Which is greater, 20·34 or 20÷34? Explain.
Answer:
Step-by-step explanation:
The result of 20 · 34 is 680, and the result of 20 ÷ 34 is approximately 0.588235294117647. Therefore, 20 · 34 is greater than 20 ÷ 34.The symbol "·" is used for multiplication, and the symbol "÷" is used for division. When we multiply 20 and 34, we are finding the total value of 20 items that are each worth 34. While when we divide 20 by 34, we are finding out how many times 34 can fit into 20, which is less than one.In short, Multiplication gives a bigger value than division, that's why 20*34 is greater than 20/34.
Answer:
Step-by-step explanation:
Hello! The way you can figure this question out is by solving each one. Let's start with 20 x 34.
How you can multiply 20 x 34
34
x20
______
00 - 0 x 4, 0 x 3 both equal 0
+ 680 - Put a 0 to the right of the number, 2 x 4 = 8, 3 x 2 = 6
______
680
34 x 20 = 680
Now, divide 20 by 34
20/34 = 10/17
10/17 is less than 1, while 680 is much greater than 1.
680 > 10/17
20 x 34 is greater than 20 divided by 34
Fun fact:
If two numbers are greater than 1, are whole numbers, and they are multiplied and divided, the number produced by each equation will always be greater when multiplied.
what is the equation of the line that passes through the point (−1,1)(−1,1) and has a slope of 5?
Answer:
The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the line has a slope of 5 and passes through the point (-1,1) we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1)
The point (-1,1) can be plugged into the equation:
y - 1 = 5(x + 1)
By simplifying and re-arranging the equation, we get:
y = 5x + 6
So the equation of the line that passes through the point (-1,1) and has a slope of 5 is: y = 5x + 6
Answer:
y = 5x+6
Step-by-step explanation:
Using the slope-intercept form of a line
y = mx+b where m is the slope and b is the y-intercept
y = 5x+b
Substitute the point into the line.
1 = 5(-1) +b
1+5 = b
6=b
The equation is
y = 5x+6
−2>m/6−7 graph the iniquality how do you do this????
A graph of the inequality is shown in the image attached below.
How to graph the inequality?In this scenario, we would solve the given inequality by making m the subject of formula as follows;
-2 > m/6 - 7
By collecting like terms, we have the following:
-2 + 7 > m/6
5 > m/6
Cross-multiplying, we have:
30 > m
By re-writing the inequality, we have:
m < 30
Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Also, the circle is open because of the greater than (>) symbol.
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a cypress beam found in the tomb of sneferu in egypt contained 55% of the amount of carbon-14 found in living cypress wood. estimate the age of the tomb given that carbon-14 has a half-life of 5730 years.
The estimated age of the tomb of Sneferu is 8,330 years.
The age of the tomb can be estimated using the carbon-14 decay equation, which states that the amount of carbon-14 remaining after time t (in years) is equal to the initial amount of carbon-14 multiplied by 0.5^(t/5730).The decay equation for carbon-14 is A = A₀e⁻kt, where A₀ is the original amount of carbon-14, A is the amount of carbon-14 at time t, k is the decay constant, and t is the amount of time that has passed.
We can rearrange the equation to solve for t: t = -ln(A/A₀)/k. In this equation, A is the amount of carbon-14 found in the cypress beam, and A₀ is the amount of carbon-14 found in living cypress wood.
In this case, the initial amount of carbon-14 was 100%, and the remaining amount was 55%. Solving for t, we get t = (ln(55%)/ln(0.5))*5730 = 8,330 years.
Therefore, the estimated age of the tomb of Sneferu is 8,330 years.
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How many solutions can be found for the system of linear equations represented on the graph?
Responses
A infinitely many solutionsinfinitely many solutions
B two solutionstwo solutions
C one solutionone solution
D no solution
Answer:
the answer is b
Step-by-step explanation:
A restaurant used 2 1/2 kilograms of potatoes to
make 6 meals. If they used an equal amount of
potatoes on each meal, how much potato did they
use for each meal?
Based on the information provided, it can be concluded that for each meal the restaurant used 0.4166 kilograms of potato.
How to calculate how many kilograms of potatoes the restaurant used in each meal?To calculate the quantity of potatoes used, you can use the following formula shown below:
Total of potatoes used / number of meals
2 1/2 kilograms of potatoes/ 6 meals
2 1/2 kilograms of potatoes is equivalent to 2.5 (1/2 = 0.5)
2.5 kilograms of potatoes/ 6 meals
0.4166
Therefore for each meal, the restaurant used 0.4166 kilograms of potatoes.
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If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), use Formula 5 of this theorem to find d/dt [u (t) x v (t). (3t sin(3 t) - cos(3 t) + 3cos(6 t), 3t- 3 sin(6 t), 3 t sin(3 t) - cos(3 t)
If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).
Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)
Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:
du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)
= (3 cos 3t, -3 sin 3t, 1)
dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)
= (1, -3 sin 3t, 3 cos 3t)
Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)
= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)
= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)
= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))
The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).
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When does king become the most emotional ? What is the message at this moment?
King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.
In what ways does Dr. King use emotion in his speech?Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.
When does king become the most emotional?King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.
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b. What is the probability that the boys will draw matching blocks? Is the game fair? Justify your answer.
yes it is fair The probability of drawing matching blocks is 1/3
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of drawing matching blocks is 1/3
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen.
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13. You need to make 18 one-cup bags of trial mix for a class trip. The recipe calls for peanuts,
chocolate chips, and raisins in the extend ratio of 5:1:4. How many cups of each item do you
need? You will get some decimal answers.
The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.
How to calculate the number of cups of each item that is needed?From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4
Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.
5x- peanuts
1x- chocolate chips
4x- raisins
5x + 1x + 4x= 18
10x= 18
x= 18/10
x = 1.8
Chocolate = 1.8 cups
Raisins = 4x
= 4 × 1.8
= 7.2 cups.
Peanut = 5x
= 5 × 1.8
= 9 cups
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the length of the diagonal AC and BD of a rhombus ABCD are 6m and 8cm, Find the length of each side of the rhombus
Length of side of the rhombus is 5cm.
Find the length of each side of the rhombus?A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.
step1
Diagonals of a rhombus bisect each other at right angles.
Let point of intersection of diagonals be O
So, OD = 3cm , OA = 4cm
From Right angled triangle △ AOD,
⇒ AD² = OA² + OD² (Pythagoras theorem)
⇒ AD² =4² + 3²
⇒ AD² = 16+9
⇒AD² =25
step2
⇒ AD² =25
⇒ AD=5 cm
AD is side of the rhombus.
So, length of side of the rhombus is 5cm
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01
3
✓5
Check
Unit price for the 2.24-pound bag:
$per pound
Unit price for the 3.12-pound bag: $ per pound
The better buy:
O The 2.24-pound bag
O The 3.12-pound bag
O Neither (They have the same unit price)
The better buy for the shrimp based on the information will be the A. 2.24 pound bag.
How to calculate the unit price?From the information, Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store and the following week, he paid $17.24 for a 3.12 -pound bag at another store.
The unit price when Josh paid $11.96 for a 2.24 -pound bag of shrimp will be:
= $11.96 / 2.24
= $5.34
The unit price when he paid $17.24 for a 3.12 -pound bag at another store will be:
= $17.24 / 3.12
= $5 53
Therefore, A is cheaper.
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Complete question
Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store. The following week, he paid $17.24 for a 3.12 -pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.