a store sells trail mix in a 5-pound bag. one serving of trail mix is 114 grams. 1 pound ≈ 454 grams. what is the approximate number of servings in a 5-pound bag of trail mix, rounded to the nearest tenth?

Answer:

60 inches

Step-by-step explanation:

In diagram A, the perimeter (outer edge) is made of 16 sides of the boxes.

48/16=3, so each side is 3 inches.

In diagram B, the perimeter is made of 20 sides.

20x3=60

In the survey on students, the probability that the student prefers to read using an electronic device is 0.46 or 46%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A survey asked students whether they preferred to read on paper (P) or using electronic devices (E).

Based on the survey, if a junior or senior is selected at random. Here,

Thus, the probability that the student prefers to read using an electronic device is,

[tex]P=\dfrac{110}{240}\\P=0.46[/tex]

Thus, in the survey on students, the probability that the student prefers to read using an electronic device is 0.46 or 46%.

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Step-by-step explanation:

125°/360°×π×15²

=245.44cm²

Answer:

3.  [tex]\dfrac{4}{3 \pi}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\dfrac13\pi r^2h[/tex]

(where r is the radius and h is the height)

Given:

[tex]\implies r=\dfrac14h[/tex]

Therefore, substitute [tex]r=\frac14h[/tex] into the volume formula to find the volume of the cone in terms of h:

[tex]\implies V=\dfrac13\pi \left(\dfrac14h\right)^2h[/tex]

[tex]\implies V=\dfrac{1}{48}\pi h^3[/tex]

Differentiate with respect to h:

[tex]\implies \dfrac{dV}{dh}=3 \cdot \dfrac{1}{48} \pi h^2=\dfrac{\pi h^2}{16}[/tex]

Volume is increasing at a constant rate of 3cm/s:

[tex]\implies \dfrac{dV}{dt}=3[/tex]

Use the chain rule to find [tex]\dfrac{dh}{dt}[/tex]

[tex]\implies \dfrac{dh}{dt}=\dfrac{dV}{dt}\times\dfrac{dh}{dV}[/tex]

[tex]\implies \dfrac{dh}{dt}=3\times\dfrac{16}{\pi h^2}[/tex]

[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi h^2}[/tex]

When h = 6:

[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi \cdot 6^2}=\dfrac{4}{3 \pi}[/tex]

Answer:

x = -9, -3

Step-by-step explanation:

[tex] {x }^{2} + 12x + 27 = 0[/tex]

[tex](x + 3)(x + 9) = 0[/tex]

x = -3, -9

Answer:

-3 and -9

Step-by-step explanation:

Standard quaratic form: a² + bx + c = 0

x² + 12x + 27 = 0

find 2 numbers that multiply to 27 (the c-value), but add to 12(the b-value);

The numbers will be 9 and 3, since;

9 x 3 = 27

9 + 3 = 12

Now we can put these numbers in the standard factor form: (x + p) (x + q);

(x + 9) (x + 3) = 0

Now we can set each part equal to 0 and solve;

x + 9 = 0  => x = -9

x + 3 = 0  => x = -3

So the roots are;

-3 and -9

Hope this helps!

Answer:

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Step-by-step explanation:

no

The length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles XYT and X'Y'T are similar to the AA Similarity Theorem

[tex]\dfrac{XT}{YT}=\dfrac{X'T}{Y'T}[/tex]

substitute the given values

[tex]\dfrac{8}{YT}=\dfrac{6}{9}[/tex]

[tex]YT=\dfrac{9\times 8}{6}[/tex]

[tex]YT=12\ units[/tex]

Hence the length of segment YT will be equal to 12 units as the line segment XY is dilated to create line segment X'Y' using point t as the center of dilation.

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Answer:

b

Step-by-step explanation:

took the test

Answer:

Height = 18 units

Step-by-step explanation:

Given :

Volume= 162pi, radius= 3 units

We know,

Volume of Cylinder= Pi * (radius)^2*h

now you can substitute, (P.S: dont put the value of pi as it will get cancelled)

162 pi = pi* (3)^2* h

162= 9h

∴h= 162/9= 18

∴ height is 18 units.

Hope it helps. But I am not sure if the answer is correct or not.

Answer:

[tex]v = \pi \: {r}^{2} h \\ where \: v = 162\pi \: \\ r = 3 \\ h = \frac{v}{ {r}^{2} } \\ h = \frac{162}{9} \\ h = 18 units[/tex]

[tex]~~~~~\pi r^2 = 513\\\\ \implies r = \sqrt{\dfrac{513}{\pi}}\\\\ \implies r= \sqrt{\dfrac{513}{3.14}}\\\\\implies r=12.78~ \text cm.}\\\\\text{Hence the radius is 12.78 cm.}[/tex]

Answer:

Step-by-step explanation:

Area of circle = πr²

[tex]\sf \boxed{r =\sqrt{ \dfrac{Area}{3.14}}}[/tex]

[tex]\sf r =\sqrt{\dfrac{513}{3.14}}\\\\r = \sqrt{163.38}\\\\r = 12.78 \ cm[/tex]

Answer:

15.4

Step-by-step explanation:

[tex]\frac{u}{4}[/tex] = tan51.3° ⇒ u = 4tan51.3° ≈ 5

[tex]\frac{4}{v}[/tex] = cos51.3° ⇒ v = [tex]\frac{4}{cos51.3}[/tex] ≈ 6.4

P ≈ 4 + 5 + 6.4 = 15.4

The perimeter of the triangle is 18.56.

The perimeter of the triangle is addition of all three sides.

Given:

The sides of angle is 4, u and v.

The angle of triangle is 51.3 degree.

For finding the value of u and v.

               [tex]tan\theta=\frac{opposite}{Adjacent}[/tex]

tan 51.3 = u/4

1.682 =u/4

u = 6.72

             [tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]

cos 51.3 = 4/v

0.51 = 4/v

v = 7.84

Perimeter = u + v + 4

                 = 6.72 + 7.84 + 4

                 = 18.56.

Therefore, the perimeter of this triangle is 18.56.

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Step-by-step explanation:

x = 5

x = -7

x = 18

x = 14

these are the answers, comment if you still have doubts.

Answer:

361

Step-by-step explanation:

it's 361 :)........

Answer:

8in³

Step-by-step explanation:

Volume is given as the product of surface area and height.

V=Ah

Where h is height and A is surface area. Here, the surface area is given 1 square inches and the height is 8 inches then the volume will be given as

V=1*8=8 cubic inches

Therefore, the volume of the bird feeder is equal to 8 cubic inches

Answer:

Measure the height of the cushion if you are covering a box cushion. Multiply the width of the cushion by two and the depth of the cushion by two, and add those numbers together to figure out how much fabric you will need to make the sides, front and back of the box cushion. Add 2 inches for seam allowances.

Step-by-step explanation:

The given expression is equivalent to 2.0x-32.

We have given that

4(0.5x-8)

We have to determine the equivalent expression.

We have to use the distributive property here

a(b+c)=ab+ac

Therefore, by using the distributive property we have,

4(0.5x-8)=2.0x-32

Therefore the given expression is equivalent to the first option

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Answer:

a. 90

b. 40

c. 55

d. 6

e. 72

Step-by-step explanation:

a: This is a rectangle so all the full corners are 90 degrees. ABC is a corner angle.

b: 1 and 3 are the congruent angles so 3 has the same measure as 1.

C: 1 is a part of the corner, which adds up to 90 degrees. That means angle 2 and angle 1 should add up to 90. They say m<1= 35, so 90-35=55.

d. In a rectangle, the interesecting lines have the same length. AC is 12, so then DB is 12. However, DE is halfway. Half of 12=6.

e. This one has a few steps. Angle 1 is 36, and angle 2 is the other part to the 90 degree corner. 90-36= 54. That gives us angle 2. We know all angles in a triangle add up to 180 degrees. The angle across from angle 2 in the same triangle is the same value, so that is also 54. To find angle 5, it must add up to 180 degrees. 54+54+x=180, in other words. 54+54=108. 180-108=72.

Answer:

I would say its B)13.50

Step-by-step explanation:

I say this because he has to buy a ticket for each person continuously so thats why I say this is the constant term added to/ subtracted from the variable term.

Hope this helped! :)

Answer:

I do not understand either

[tex]f(x) = 5 \cdot 3^x\\\\\\f(-2) = 5\cdot 3^{-2}\\\\~~~~~~~~~=5\cdot \dfrac 1{3^2}\\\\~~~~~~~~~=\dfrac 59\\\\\text{Hence the answer is D.}[/tex]

Given : number -3/4 - and  number line​

To Find :  represent -3/4 - on number line​

Solution:

Numbers with a negative sign are less than zero

Right of zero represented by ‘+’ sign and to the left of zero represented by ‘–’ sign.

+ sign numbers can be denoted as simply numbers  

On a number line the number increases as we move to the right and decreases as we move to the left.  

1 : Draw a line and mark some points at equal distance on it

Mark a point as zero on it. Points to the right of zero are positive integers and are marked simply 1, 2, 3  and so on , while points to the left of zero are negative integers and are marked – 1, – 2, – 3 and so on

- 3/4

Divide number line between -1 & 0  in  4 Equal parts and go 3 part left of 0 to show - 3/4 on number line

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Answer:D)6

Step-by-step explanation: