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11 months ago

The formula m =1/2(a+b) gives the mean M of two numbers a and b

Mathematics

2 answers:

Semenov [28]11 months ago

7 0

Answer:

a = 2m - b , a = 15

Step-by-step explanation:

(a)

m = $\frac{1}{2}$ (a + b) ← multiply both sides by 2 to clear the fraction

2m = a + b ( subtract b from both sides )

2m - b = a

(b)

when m = 19 and b = 23 , then

a = 2(19) - 23 = 38 - 23 = 15

Viefleur [7K]11 months ago

6 0

Answer:

Step-by-step explanation:

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On the graph below are three points X, Y, and Z. Write the coordinates for the given dilation.

Julli [10]

ANSWER

$( - \frac{3}{2} , - 1)$

EXPLANATION

From the graph, the coordinates of Y are:

$(3,2)$

We want to find the image of this point after a dilation by a scale factor of -½ about the origin.

The rule for the dilation is :

$(x,y)\to( - \frac{1}{2} x, - \frac{1}{2} y)$

To find the coordinates of Y', we plug the coordinates of Y.

$Y(3,2)\to \: Y'( - \frac{1}{2} (3), - \frac{1}{2}(2) )$

$Y(3,2)\to \: Y'( - \frac{3}{2}, - 1)$

The first choice is correct.

6 0

2 years ago

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or

Irina18 [472]

Answer:

4) i) The numbers can represent the side lengths of a triangle

ii) Right triangle

5) i) The numbers can represent the side lengths of a triangle

ii) Isosceles triangle

6) i) The numbers can represent the lengths of the sides of a triangle

ii) Pythagoras theorem

7) The numbers do not represent the lengths of sides of a triangle

8) i) The numbers can represent the side lengths of a triangle

ii) Scalene triangle

Step-by-step explanation:

In a triangle, the sum of the lengths of the two shorter sides is longer than the length of the longest side

The given numbers are;

4) i) 15, 20, 25

Given that 15 + 20 < 25, the numbers can represent the side lengths of a triangle

ii) 15² + 20² = 25²

Therefore, the sides lengths are in line with the side length of a right triangle as their relation is given by Pythagoras theorem

The triangle is a right triangle

5) i) The given numbers are;

2, 6, 6

Given that 2 + 6 > 6, the numbers can represent the side lengths of a triangle

ii) Given that the lengths of two sides are equal (6 each), the triangle formed by the numbers is an isosceles triangle

6) i) 0.27, 0.36, 0.45

0.27 + 0.36 = 0.63 > 0.45, therefore, the numbers can represent the lengths of the sides of a triangle

ii) Given that 0.27² + 0.36² = 0.45², according to Pythagoras theorem, the type of triangle formed is a right triangle

7) 2.5, 1.5, 4

Given that 2.5 + 1.5 = 4, the numbers do not meet the criteria for forming triangles and therefore they cannot represent the side lengths of a triangle

8) i) 12, 16, 25

12 + 16 = 28 > 25, the numbers can represent the side lengths of a triangle

ii) 12² + 16² = 400 < 25² = 625, therefore, the triangle formed by the numbers is not a right triangle but a scalene triangle.

7 0

2 years ago

An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-tempera

Olin [163]

Answer:

(115.2642, 222.7358).

Step-by-step explanation:

Given data:

type A: n_1=60, xbar_1=1827, s_1=168

type B: n_2=180, xbar_2=1658, s_2=225

n_1 = sample size 1, n_2= sample size 2

xbar_1, xbar_2 are mean life of sample 1 and 2 respectively. Similarly, s_1 and s_2 are standard deviation of 1,2.

a=0.05, |Z(0.025)|=1.96 (from the standard normal table)

So 95% CI is

(xbar_1 -xbar_2) ± Z×√[s1^2/n1 + s2^2/n2]

=(1827-1658) ± 1.96×sqrt(168^2/60 + 225^2/180)

= (115.2642, 222.7358).

8 0

2 years ago

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what

Citrus2011 [14]

<em>The complete exercise with the answer options is as follows:</em>

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust 364

Thick crust 240

Stuffed crust 176

Pan style 260

Based on this information, of the next 3000 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer:

692 thick crust pizzas

Step-by-step explanation:

With the data given in the exercise, we must first find the total number of pizzas, then we must find the proportion between the thick crust pizzas and the total number of pizzas, finally we must propose a rule of three to find the new proportion of crust pizzas thick on a total of 3000 pizzas.

Type of Crust Number Sold

Thin crust 364

Thick crust 240

Stuffed crust 176

Pan style 260

total pizzas : 1040

Now we must calculate for 3000 pizzas how much would be the total of thick crust pizzas.For that we must use the relationship found, that is, in 1040 pizzas there are 240 thick crust pizzas

1040→240

3000→x

x= $\frac{3000x240}{1040}$ = 692

Now we have a new proportion that out of 3000 pizzas there are a total of 692 thick crust pizzas

3 0

2 years ago

Can you guys please help me my math teacher wants us to get this right and I don’t get it please help me on all of it

Ostrovityanka [42]

#5 is

Let's solve your equation step-by-step.

x−1=9

Step 1: Add 1 to both sides.

x−1+1=9+1

x=10

Step 2: Multiply both sides by 5/2.

(

)*(

x)=(

)*(10)

x=25

Answer:

x=25

7 0

2 years ago