A researcher carefully calculates the correlation coefficient and gets a value of r=1.23. What does this value mean?

Bananas are being sold for $0.59 a pound at Store A and $0.55 a pound at Store B. A customer wants to buy 10 pounds of bananas.

andre [41]

Answer:

The customer saves 5.9 - 5.5 = $0.5

when he shops at store B

Step-by-step explanation:

Stores A and B sells bananas at different prices per pound.

Bananas are being sold for $0.59 a pound at Store A and $0.55 a pound at Store B.

If a customer wants to buy 10 pounds of bananas from store A and store B,

The customer would spend 0.59 × 10 pounds of bananas = $5.9

buying from store A and

The customer would spend 0.55 × 10 pounds of bananas = $5.5

buying from store B.

The customer spends more for 10 pounds of bananas if he buys from shop A.

The customer saves 5.9 - 5.5 = $0.5

when he shops at store B

8 0

2 years ago

In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .

⇒ $\cos Z =\frac{3.5}{18}$

⇒ $\cos Z = 0.195$ (approx) or

$Z=\cos^{-1}(0.195)$

Therefore, the angle $\angle Z = 78.7^{\circ}$ .

The sum of the measure of the angle in the triangle is 180 degree.

In triangle XYZ.

$\angle X +\angle Y+\angle Z =180^{\circ}$

Since $\angle X=\angle Z =78.7^{\circ}$

then,

$78.7^{\circ}+\angle Y+78.7^{\circ}=180^{\circ}$

⇒ $157.4^{\circ}+\angle Y=180^{\circ}$

Simplify:

$\angle Y=22.6^{\circ}$ .

Therefore, the measure of each angle are: $\angle X=\angle Z=78.7^{\circ}$ and $\angle Y =22.6^{\circ}$

8 0

2 years ago

The scale for the drawing of a rectangular playing field is 2 inches= 5 feet. Write an equation you can use to find the dimensio

iris [78.8K]

Answer:

Step-by-step explanation:

Given:

Scale

2 inches : 5 feet

Actual dimensions

Let x be the dimension of the scale drawing (in inches) and y, the corresponding dimension of the actual field (in feet).

Scaled dimension = scale × actual dimension

Actual dimension, x = y × 5 ft/2 in

2 × x = 5 × y

Equation:

2x = 5y

3 0

2 years ago

Write the quadratic equation whose roots are

maks197457 [2]

The quadratic equation $y = ax^2 +bx+c$ can be written in the form:
$y = a(x-p)(x-q)$
Where p and q are the roots of the equation.
Given p = 4, q = -2, a = 3, the quadratic will look like this:
$y = 3(x-4)(x+2)$
Finally, distribute and combine like terms to put it in standard form.
$y = 3(x^2 - 4x+2x -8) \\ \\ y = 3(x^2 -2x-8) \\ \\ y = 3x^2 -6x -24$

5 0

2 years ago

6d - e + 3d - 2e<br><br>( combine like terms)

Alenkasestr [34]

6d and 3d are like terms, so you take them and add them together because they're both positive. You get 9d-e-2e. -e and -2e are also like terms so you would put these together but subtract them to get 9d-3e.

6 0

2 years ago

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