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LiRa [457]
2 years ago
14

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the

value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
Mathematics
2 answers:
RoseWind [281]2 years ago
3 0
Well, there are x amounts of white flower and 6 cups of wheat flower.

So the total flower is x+6

Given that y is the total, the equation you would use is:
y=x+6

The constraints are as follows:
y can only be \geq 6

And if y=0, x would have to be -6 (which is impossible) 
Dmitrij [34]2 years ago
3 0

Answer:

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

You might be interested in
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3
Komok [63]
base 16y^2
height y^2 + y + 3
V = b*h
V = 16y^2(y^2 + y + 3)
V = 16y^4 + 16y^3 + 48y^2
Last option
6 0
1 year ago
Read 2 more answers
What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24
shusha [124]

The value of b is -6.

Explanation:

The expression is \left(y^{b}\right)^{4}=\frac{1}{y^{24}}

To determine the value of b, we shall solve the expression.

Applying exponent rule, \left(a^{b}\right)^{c}=a^{b c}, we get,

y^{4b}=\frac{1}{y^{24}}

Applying exponent rule, \frac{1}{a^{b}}=a^{-b}, we have,

y^{4b}=y^{-24}

The expression is of the form, a^{f(x)}=a^{g(x)} then f(x)=g(x)

Applying this rule, we get,

4b=-24

Dividing both sides by 4, we have,

b=-6

Hence, the value of b is -6.

4 0
2 years ago
Read 2 more answers
Find the distance from (4, −7, 6) to each of the following.
LenKa [72]

Answer:

(a) 6 units

(b) 4 units

(c) 7 units

(d) 9.22 units

(e) 7.21 units

(f) 8.06 units

Step-by-step explanation:

The distance d from one point (x₁, y₁, z₁) to another point (x₂, y₂, z₂) is given by;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Now from the question;

<em>(a) The distance from (4, -7, 6) to the xy-plane</em>

The xy-plane is the point where z is 0. i.e

xy-plane = (4, -7, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, -7, 0)</em>

d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

d = √[(0)² + (0)² + (-6)²]

d = √(-6)²

d = √36

d = 6

Hence, the distance to the xy plane is 6 units

<em>(b) The distance from (4, -7, 6) to the yz-plane</em>

The yz-plane is the point where x is 0. i.e

yz-plane = (0, -7, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, -7, 6)</em>

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Hence, the distance to the yz plane is 4 units

<em>(c) The distance from (4, -7, 6) to the xz-plane</em>

The xz-plane is the point where y is 0. i.e

xz-plane = (4, 0, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, 0, 6)</em>

d = √[(4 - 4)² + (-7 - 0)² + (6 - 6)²]

d = √[(0)² + (-7)² + (0)²]

d = √[(-7)²]

d = √49

d = 7

Hence, the distance to the xz plane is 7 units

<em>(d) The distance from (4, -7, 6) to the x axis</em>

The x axis is the point where y and z are 0. i.e

x-axis = (4, 0, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, 0, 0)</em>

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x axis is 9.22 units

<em>(e) The distance from (4, -7, 6) to the y axis</em>

The x axis is the point where x and z are 0. i.e

y-axis = (0, -7, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, -7, 0)</em>

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

d = √[(4)² + (0)² + (6)²]

d = √[(4)² + (6)²]

d = √[(16 + 36)]

d = √(52)

d = 7.22

Hence, the distance to the y axis is 7.21 units

<em>(f) The distance from (4, -7, 6) to the z axis</em>

The z axis is the point where x and y are 0. i.e

z-axis = (0, 0, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, 0 6)</em>

d = √[(4 - 0)² + (-7 - (0))² + (6 - 6)²]

d = √[(4)² + (-7)² + (0)²]

d = √[(4)² + (-7)²]

d = √[(16 + 49)]

d = √(65)

d = 8.06

Hence, the distance to the z axis is 8.06 units

5 0
2 years ago
Consider the midterm and final for a statistics class. Suppose 13% of students earned an A on the midterm. Of those students who
padilas [110]

Answer:

There is a 38.97% probability that this student earned an A on the midterm.

Step-by-step explanation:

The first step is that we have to find the percentage of students who got an A on the final exam.

Suppose 13% students earned an A on the midterm. Of those students who earned an A on the midterm, 47% received an A on the final, and 11% of the students who earned lower than an A on the midterm received an A on the final.

This means that

Of the 13% of students who earned an A on the midterm, 47% received an A on the final. Also, of the 87% who did not earn an A on the midterm, 11% received an A on the final.

So, the percentage of students who got an A on the final exam is

P_{A} = 0.13(0.47) + 0.87(0.11) = 0.1568

To find the probability that this student earned an A on the final test also earned on the midterm, we divide the percentage of students who got an A on both tests by the percentage of students who got an A on the final test.

The percentage of students who got an A on both tests is:

P_{AA} = 0.13(0.47) = 0.0611

The probability that the student also earned an A on the midterm is

P = \frac{P_{AA}}{P_{A}} = \frac{0.0611}{0.1568} = 0.3897

There is a 38.97% probability that this student earned an A on the midterm.

5 0
2 years ago
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Volgvan

Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : H_0:\mu\geq 50000

Alternate hypothesis : H_1:\mu

There  is 5% level of significance.

\bar{X}=46800\\\\\sigma=9800\\\\n=29

So, the test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

So, we reject the null hypothesis, and we use Normal distribution for the test.

4 0
2 years ago
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