Answer: To determine which expression is equivalent to 3√/8x²y³ z^4, we need to simplify the given expression and compare it with the options.
First, we can simplify the cube root:
3√/8x²y³ z^4 = (3/8)x^(2/3)y^(1/3)z^(4/3)
Now, we can compare this expression with the options:
A. 2x^(3/2)YZ^(3/4) is not equivalent to the simplified expression because the exponent of x is different (3/2 vs 2/3)
B. 2x^(2/3)YZ^(3/4) is equivalent to the simplified expression. The exponents of x, y and z are the same and the coefficient is also the same
C. 2z/x is not equivalent to the simplified expression because it has different variables and exponents
D. 2x/z is not equivalent to the simplified expression because it has different variables and exponents
Therefore, the expression that is equivalent to 3√/8x²y³ z^4 is B. 2x^(2/3)YZ^(3/4)
Step-by-step explanation:
if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is
we have distance from focus to its vertex =p, then distance between focus to directrix = p + p=2p
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.
Since the distance between the vertex and the focus is the same as the distance between vertex to directrix,
So, we have distance from focus to its vertex =p
then distance between focus to directrix = p + p=2p
The complete question is:-
if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is equal to?
(a) p (b) 2p (c) p+1 (d) p/2.
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The drawing shows an isosceles triangle. 65° Work out the size of angle a. 23/196 a
In the isosceles triangle, the size of angle, a is 50°
What is isosceles triangle?An isosceles triangle is a type of triangle which has two sides that are equal in length.
This type of triangle has two angles which are the same and the third angle is different from the other two. It also has three sides, with two sides being equal and the third side being different.
The base of the isosceles triangle is the side that has two equal sides, and the sides that are equal are called the legs. The angles that are equal are called the base angles. The point at which the two equal sides meet is called the vertex.
The angles of the isosceles triangle add up to 180 degrees. The base angles are the same, while the third angle is different and can be greater or smaller than the other two angles. This type of triangle is very symmetrical, as the two equal sides create a mirror image of the triangle.
Isosceles triangles are very useful in many areas, such as mathematics, engineering and architecture. In mathematics, isosceles triangles are used to solve problems involving angles, area, and perimeter.
In engineering, they are used in many structures such as bridges. In architecture, they are used to create aesthetically pleasing designs for buildings and monuments.
Given, one side of angle is 65°
For isosceles triangle two sides of angles are equal.
A triangle always have 180°
a + b + c = 180°
a = 180° - 65° - 65°
a = 50°
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determine if one of the given vectors is in the span of the other vectors. (hint: check to see if the vectors are linearly dependent, and then appeal to this theorem.) u=[1,7,8,3] v=[-1,3,5,3]
w=[4,8,6,0]
a. None of the vectors is in the span of the other vector.
b. One of the vectors is in the span of the other vector
Out of the given vectors is in the span of the other vectors, b. One of the vectors is in the span of the other vector. Since u and v have the same last component, they are linearly dependent, so u is in the span of v and w.
If a set of vectors is linearly dependent, then one of the vectors can be expressed as a linear combination of the other vectors. This means that one vector is in the span of the other vectors. In this case, u can be expressed as a linear combination of v and w, so u is in the span of the other vectors.
To check for linear dependence, we can first check for a zero row in the matrix formed by the vectors. If there is a zero row, then the vectors are linearly dependent. In this case, the last row of the matrix formed by the vectors is [3,3,0], which is a zero row, so the vectors are linearly dependent. We can also check for linear dependence by computing the determinant of the matrix formed by the vectors.
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Can anyone help??
Which line is parallel to y=-4x+11 and goes through (2,1)? Hint: use point slope form
A)y-1=-4x(x-2)
B)y-1=-1/4(x-2)
C)y-1=4(x-2)
D)y-2=-4(x-1)
(I’m trying to do test corrections :c )
A line that is parallel to y = -4x + 11 and goes through the point (2, 1) in point slope form is: A. y - 1 = -4(x - 2).
What is the point-slope form?Mathematically, the point-slope form of a line is modeled by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 11, the slope is given by:
y = -4x + 11
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (2, 1), an equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 2)
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In 2015, as part of its 10th high school reunion, the class of 2005 held a reception at the high school. In an informal survey, the principal of the high school asked 50 of the attendees about their income. The principal computed the mean income of the 50 attendees to be $148,535. In an article published by the local newspaper, the principal was quoted as stating, "The members of our class of 2005 enjoyed resounding success. Last year, they had a mean income of $148,535!"
Part A: What is a statistical advantage of using the median of the reported incomes, rather than the mean, as the estimate of the typical income? (4 points)
Part B: The principal felt the individuals who attended the reception may be different from the class as a whole. A more detailed survey of the class was planned to determine a better estimate of income. The staff developed two methods based on the available funds to carry out the survey.
Method 1: Send out an e-mail to all 2,476 members of the class and ask them to complete an online form. The staff estimates that at least 500 members will respond.
Method 2: Select a simple random sample of members of the class and contact the selected members directly by phone. Follow up to ensure all responses are obtained. Because method 2 requires more time than method 1, the staff estimates only 100 members of the class can be contacted using method 2.
Which of the two methods would you select for estimating the average yearly income of all 2,476 members of the class of 2005? Explain your reasoning by comparing the two methods and by describing the effect of each method on the estimate.
Method 2 is the best option for estimating the average yearly income of the class of 2005.
What type of sampling technique is used?I would select Method 2 for estimating the average yearly income of all 2,476 members of the class of 2005. Method 2 involves selecting a simple random sample of members of the class and contacting them directly by phone. This method guarantees that the sample will be representative of the entire population and thus provides the best estimate of the average income of the class. By randomly selecting the sample, we can be sure that the sample will be unbiased and the results will be more reliable. Method 1, on the other hand, involves sending an e-mail to all 2,476 members of the class and asking them to complete an online form. Although this method is easier and less time-consuming, it does not guarantee a representative sample. If only 500 people respond, it is possible that the sample will not be representative of the entire population and thus, the results will not be accurate. Overall, It will ensure that the sample is representative of the entire population and that the results are unbiased and reliable.To learn more about the sampling theory refer to:
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Help me ASAP math question.
The trip was 18 minutes and they travelled 6 miles.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From the given information we form system of equations
0.2x+1.5y+5=17.60..(1)
x-3y=0
x=3y..(2)
Plug 2 in equation 1
0.2(3y)+1.5y+5=17.6
0.6y+1.5y=12.6
2.1y=12.6
Divide both sides by 2.1
y=6
x=3(6)=18
Hence, the trip was 18 minutes and they travelled 6 miles.
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6= 1/v+2
Solve for V
simplify your answer as much as possible
Answer:
your question is 6=1/v+2
Step-by-step explanation:
6-2=1/v
4v=1
v=1/4
Guys pls help me fast rapidly is of math:
For the given equation, the binomial factor is (5x² + 3).
In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y
How do binomial factors work?Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.
5x³ - 25x² + 3x - 15
Taking 5x² and 3 as common factors -
⇒ 5x² (x - 5) + 3 (x - 5)
GCF of 1 step is 5x²
⇒ (5x² + 3) (x - 5)
GCF of 2 step is 5x² + 3
Common binomial factor is (5x² + 3)
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Evaluate the expression using the given value of the variable:[ y + z - z ]; use [y = 6], and [z = 5] .
Answer:
( y + z - z )
given, y= 6 z=5
(6 + 5 - 5 )
Use DMAS rule
D=division M= multiplication A= addition S=subtraction
(11-5)
6 (ans)
Please help! Systems of equation/matrix problem
5. TELEVISION During t
ring the summer, Manuel watches television M hours per day, Monday through Friday. Harry watches television H hours per day, Friday and Saturday. Ellen watches television E hours per day, Friday through
Sunday. Altogether, they watch television 37 hours each week. On Fridays, they watch a total of 11 hours of television.
If the number of hours Ellen spends watching television on any given day is twice the number of hours that Manuel
spends watching television on any given day, how many hours of television does each of them watch each day?
Answer:
see attached
Step-by-step explanation:
If angle A=−170∘, what is the radian measure of A? Enter an exact fraction that contains the π symbol.
The radian measure of A = 170° as an exact fraction that contains the π symbol is; ¹⁷/₁₈π
How to convert degrees to radians?When we want to convert the value of an angle in degree, to its equivalent radians, what we need to do is to multiply the given value with π/180. For example, the value of 180 degrees is π in radians.
Thus, since we want to find the radian measure of 170 degrees, it means that;
If 180° = π radians,
then; 170° = (170 * π)/180
= ¹⁷/₁₈π
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use the empirical rule. sketch the values and calculate the z scores. a) approximately what percentage of the observations fall between 32 and 48?
Approximately 95.45% of the observations fall between 32 and 48.
Using the Empirical Rule, we can calculate the Z scores for 32 and 48 to see what percentage of observations falls between these values.
First, calculate the Z score for 32:
Z = (32 - 40) / 4 = -2
Next, calculate the Z score for 48:
Z = (48 - 40) / 4 = 2
The Empirical Rule states that approximately 68% of the observations fall within 1 standard deviation of the mean, which is between 36 and 44 in this case. However, since the Z scores for 32 and 48 are both outside of this range, we need to calculate the percentage of observations that falls between these Z scores.
Using a standard normal distribution table, we can see that the percentage of observations between Z = -2 and Z = 2 is approximately 95.45%. This means that approximately 95.45% of the observations fall between 32 and 48.
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--The given question is incomplete; the complete question is
"Data are drawn from a normal distribution with a mean of 40. the standard deviation of 4. Use the Empirical Rule. SKETCH the values and calculate the Z scores. a) Approximately what percentage of the observations fall between 32 and 48?"--
two expressions that are equivalent to 3f
The two expressions are written as :
3f + 2f + 4s 5f + 4sHow to solve for the expressions that are equivalent to 3f+4s+2f3f+4s+2f this expression that we have here is a mathematical expression that we can combine by making use of the commutative addition.
We would have the first expression when we write the equation as:
3f+4s+2f = 3f + 2f + 4s
We would have the second expression when we write the equation as
5f + 4s
This is the solution of the expression.
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two expressions that are equivalent to 3f+4s+2f ?
graph an equation of the form y=kx+1 which includes point m. m(2,-7)
The linear equation y = - 4 · x + 1 includes point (x, y) = (2, - 7).
How to graph a linear function on Cartesian plane
In this problem we need to plot a linear equation on Cartesian plane, linear equations are first polynomials of the form:
y = m · x + b
Where:
x - Independent variabley - Dependent variablem - Slopeb - InterceptIf we know that b = 1 and (x, y) = (2, - 7), then the equation of the line is:
- 7 = 2 · k + 1
- 8 = 2 · k
k = - 4
y = - 4 · x + 1
Now we proceed to graph the line. First, find two points of the line:
x = 0
y = - 4 · 0 + 1
y = 1
x = 1
y = - 4 · 1 + 1
y = - 3
Second, plot the points on Cartesian plane.
Third, construct the line that passes through the two points.
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HELP ME ASAP! i need help rn
Answer: yes
Step-by-step explanation:
It's right angled if and only if A^2 + B^2 = C^2
- a^2 = (11-3^2 + 11-5^2) = (64 + 36) = 100
- b^2 = (6-3^2 + 1-5^2) = (9 + 16) = 25
a^2 + b^2 = 125 = sqrt(125)^2
Debbie shipped 2 packagesone weighed 2 pounds10 ounces the other weighed 4 pounds and12 ounces what is the total weight of The 2 packages
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
what is unitary method ?The unit tactic is a strategy for addressing issues that entails first figuring out the value of a particular unit, then increasing that value to figure out the needed value. Simply put, the unit method is employed to obtain a minimum unit value from a multiple that is supplied. For example, 40 pens may cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its homologue and reciprocal are equal in terms of mathematics, algebra, linear algebra, applied mathematics, or mathematics for matrices or operators.
given
1 pound = 16 ounces
for 2 packages
2 pounds 10 ounces + 4 pounds 12 ounces
6 pounds and 22 ounces
= 7 pounds 10 pounces
The combined weight of the two parcels, one of which weighs 2 pounds 10 ounces and the other 4 pounds and 12 ounces, is 7 pounds 10 pounces.
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State if the three numbers can be the measures of the sides of a triangle. 7, 10, 10
Yes, these numbers meet the triangular inequalities, then these can be the measures of the sides of a triangle.
Can be the measures of the sides of a triangle?Remember that if A, B, and C are the sides of a triangle, then the triangle inequality says that:
A + B > C
A + C > B
C + B > A
As long as 3 values are solutions of the inequalities, then these can be the sides of a triangle.
if we use:
A = 7
B = 10
C = 10
Then we get:
7 + 10 > 10 ---> 17 > 10
7 + 10 > 10 ---> 17 > 10
10 + 10 > 7 ---> 20 > 7
All the ienqualities are true, thus, these can be the measures of the sides of a triangle.
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According to the United States Department of Health and Human Services, the mean height for Americans is 1.757m for men and 1.618 m for women3. The standard deviation is 0.074m for men and m for women.
1)
What -score corresponds to a man who is 1.853m tall?
A man who is 1.853m tall would have a z-score of 1.297.
What is the z-score?Generally, To find the z-score for a man who is 1.853m tall, we need to use the formula for a z-score:
= (x - mean) / standard deviation.
In this case, the mean height for men is 1.757m and the standard deviation is 0.074m, so the z-score for a man who is 1.853m tall would be:
(1.853 - 1.757) / 0.074 = 1.297297297
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Pls help, OR ELSE a grotesque Dung Beatle will find its way into your coffee ☕
Question
In this figure, GH=10, GP=16, and FP=4.
What is EF?
Enter your answer in the box.
EF =
Answer: EF = 12 is the correct answer.
Step-by-step explanation: EF = GP - FP = 16 - 4 = 12Given that GH=10, GP=16, and FP=4. We have to find the value of EF. We can use this formula to find it:EF = GP - FP = 16 - 4 = 12So the value of EF is 12. In the given figure, ABCD is a rectangle and GP and GH are the diagonals. EF is the length of the rectangle.Therefore, EF = 12 is the correct answer.
Answer:Well i think EF would be 10 since it looks like the same length as GH
Step-by-step explanation:
.An artist sells his paintings at a gallery. He charges a set price for each small painting K and
each large painting he sells. Last month, the artist sold 6 small paintings and 8 large
paintings and earned $670 in all. This month, he sold 12 small paintings and 10 large
paintings and earned $950 in all. How much does the artist charge for a small painting?
How much does he charge for a large painting?
I need this in system of equation form please.
The artist charges $25 for a small painting and $65 for a large painting.
How to substitute two equations?
To substitute one equation into another, you can replace one of the variables in the second equation with the expression from the first equation.
Let K be the price of small painting and L be the price of large painting.
From the information given, we know that:
Last month:
6K + 8L = $670 (1)
This month:
12K + 10L = $950 (2)
We have two equations and two unknowns, so we can use a system of equations to find the values of K and L.
Solving the system of equations:
From (1) equation, we have:
6K + 8L = $670
From (2) equation, we have:
12K + 10L = $950
Now we can solve for K (small painting) by multiplying equation (1) by 2 and equation (2) by -1 and adding the two equations together:
12K + 16L = $1340
-12K - 10L = -$950
0K + 6L = $390
Therefore, L = $390 / 6 = $65
Now we can substitute this value of L back into the first equation (1) and solve for K:
6K + 8($65) = $670
6K = $670 - 8($65) = $670 - $520 = $150
K = $150 / 6 = $25
So, the artist charges $25 for a small painting and $65 for a large painting.
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In ABCD, CD = 12, DB = 10, and BC = 6. Which list has the angles of ABCD in order from largest to smallest?
A, C, B, and D make up the list of ABCD's angles, from largest to smallest, with 90°, 54°, 24°, and 12°, respectively.
What's an angle?The sides of a triangle, or angle, are two rays that make up the figure. The Law of Cosines can be used to find Angle A. We can solve for the angle A by using the formula
c² = a² + b² - 2abcos(C).
Since we know the lengths of all sides, we can substitute in the values.
c² = 122 + 102 - 2(12)(10)cos(A)
Cos(A) = (144 + 100 - 120)/240
= 24/240
= 0.1
In the end, we use the inverse cosine to determine the angle A, which is roughly 74 degrees.
The same formula can be used to determine Angle D.
c² = 62 + 102 - 2(6)(10)cos(D)
Cos(D) = (36 + 100 - 60)/120
= 76/120
= 0.63 .
When we take the inverse cosine, we get the angle D, which is about 27.3 degrees.
The same formula can be used to determine Angle C.
c² = 122 + 62 - 2(12)(6)cos(C)
Cos(C) = (144 + 36 - 72)/144
= 108/144
= 0.75
When we take the inverse cosine, we get the angle C, which is about 36.9 degrees.
The same formula can be used to determine Angle B.
c² = 122 + 102 - 2(12)(10)cos(B) .
Cos(B) = (144 + 100 - 120)/240
= 24/240
= 0.1
We obtain the angle B, which is roughly 74 degrees, by applying the inverse cosine.
Therefore, ABCD's angles, from largest to smallest, are as follows: angle C (36.9°), angle B (74°), and angle D (27.3°)
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Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
one half comma negative 5
one half comma 5
5 comma one half
negative 5 comma one half
The solution to the simultaneous equations is; 5 comma one half
How to solve Simultaneous Linear Equations?The simultaneous equations are;
y = -¹/₂x + 3 -------(1)
y = ¹/₂x - 2 -------(2)
Substitute ¹/₂x - 2 for y in eq 1 to get;
¹/₂x - 2 = -¹/₂x + 3
Add -¹/₂x to both sides using addition property of equality to get;
¹/₂x + ¹/₂x - 2 = 3
Add 2 to both sides using addition property of equality to get;
x = 3 + 2
x = 5
Thus;
y = ¹/₂(5) - 2
y = ¹/₂
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Answer:
Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
Step-by-step explanation:
If the measure of angle is 0 is 7pi/4, which statements are true?
The measure of the reference angle is 45°.
The measure of the reference angle is 30°.
tan(0) = -1
The measure of the reference angle is 60°.
cos(0) = -â2/2
sin(0) = -â2/2
The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
The measure of an angle is the amount of rotation from the starting position to the endpoint of the angle. In this problem, the measure of angle is 0 is 7π/4. This means that the angle has rotated 7π/4 radians from the start position, which is equivalent to 360° - (7π/4)*180/π = 315°.
Therefore, the measure of the reference angle is 45°, because the reference angle is the smallest angle that starts at the x-axis and terminates at the terminal side of the angle, which in this case is 315°. The reference angle is equal to the measure of the angle minus the multiple of 360°, so 45° = 315° - 360°.
The trigonometric functions of sine, cosine, and tangent can be used to evaluate the measure of an angle. The sine of an angle is equal to the ratio of the opposite side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, sin(0) = opposite/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The cosine of an angle is equal to the ratio of the adjacent side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, cos(0) = adjacent/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The tangent of an angle is equal to the ratio of the opposite side of the angle over the adjacent side of the angle. In this problem, tan(0) = opposite/adjacent = -1, since the angle is 7π/4 radians, or 315°.
In conclusion, the measure of angle is 0 is 7π/4, and the measure of the reference angle is 45°. The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
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Find the area of this irregular figure, all angles are right angles
The area of this irregular figure is 256 square inches
How to determine the area of the figureFrom the diagram shown, we can see that the figure is composite, holding two rectangles together.
We can see that both rectangles have the same length and width measurement.
It is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
Given that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFor Rectangle A
Area = 16(8)
multiply values
Area = 128 Inches square
Rectangle B
Area = 16(8)
Area = 128 Inches square
Area of figure = 128 + 128
Area =256Inches square
Hence, the value is 256Inches square
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use theorem 2.1.13 to prove that if $f$ and $g$ are continuous functions with open domains $u f$ and $u g$, and if $g(u g)\subseteq u f$, then $f \circ g$ is continuous on $u g$
Since function f andg are continuous and u g subseteq u f, Theorem 2.1.13 states that f circ g is continuous on u g.
In accordance with Theorem 2.1.13, if two functions,f andg, are continuous on open domains [tex]$u f$[/tex]and [tex]$u g$[/tex] respectively, and $g(u g)subseteq u f, then $ circ g is continuous on u g. This is the case since the domain of f, which is u g is a subset of the domain of f, which is u g, and the composition of continuous functions is continuous. The composition of these two functions will be continuous onu g because both of these functions are continuous and u g subseteq u f.
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Patricia is making homemade snacks. Each snack requires 2.25 cups of almonds. Patricia buys 6 cans of almonds that each contain eight 1/3 cup servings. What is the maximum number of snack bags that Patricia can make with the almonds?
Answer: 7
Step-by-step explanation:
Patricia has 6 cans of almonds that each contain eight 1/3 cup servings, meaning that Patricia has a total of
6 cans x 8 servings x 1/3 cup = 16 cups of almonds
If she needs 2.25 cups of almonds, that would be equal to
16/2.25 = around 7.1
since you can't have a fraction of a snack bag, Patricia just has 7 snack bags.
a = 47.4 rounded to 1 DP
b = 0.19 rounded to 2 DP
Find the minimum of a - b
Answer:
47.21
Step-by-step explanation:
Subistitute:-47.4-0.19
Calculate the sum or difference:-47.21
the figure at the right is a regular octagon with the sign length s. Write two algebaric
The expression of the side length is 6y - 5
How to determine the expression of the side lengthThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Perimeter = 48y - 40
Number of sides = 8
The side length s can be calculated as
s =(48y - 40)/8
Evaluate the quotient
s = 6y - 5
Hence, the side length expression is 6y - 5
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I can’t figure it this problem out please help me
Angelina spent less than 15 hours practicing for her surfing competition. How many hours could she have spent surfing?