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Veseljchak [2.6K]

3 years ago

7

A bakery made 25 cherry pies, using 101 cherries for each pie. They threw away 30 cherries that were bad. If they used all the c

herries they had, how many cherries did they start off with? A. 2,525 B. 2,495 C. 2,555 D. 156

1 answer:

Alex777 [14]3 years ago

6 0

The correct answer is a

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The area of the trapezoid is 24 and the bases are 3 and 5. find the height. 3 3.2 6

lorasvet [3.4K]

<span>1. To solve this problem you must apply the formula for calcúlate the area of a trapezoid, which is shown below:

A=(B+b)h/2

A is the area of the trapezoid (A=24).
B is the larger base </span>of the trapezoid <span>(B=5).
b is the smaller base </span>of the trapezoid<span> (b=5).
h is the height </span><span>of the trapezoid.

2. You must clear "h" from the formula:
</span><span>
A=(B+b)h/2
</span> 2A=<span>(B+b)h
</span> h=2A/<span>(B+b)
</span><span>

3. When you susbtitute the values into </span> h=2A/(B+b), you obtain:

h=2A/<span>(B+b)
</span><span> h=2(24)/(5+3)
h=48/8
h=6
</span>

6 0

3 years ago

Tentukan hasil dari (tanpa menghitung satu persatu)

liubo4ka [24]

a . 1 + 3 + 5 + 7 + 9 + ... + 99 = 2500

b. 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

c. -100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50 = -3775

<h3>Further explanation</h3>

Let us learn about Arithmetic Progression.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\large {\boxed {T_n = a + (n-1)d } }$

$\large {\boxed {S_n = \frac{1}{2}n ( 2a + (n-1)d ) } }$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

Let us now tackle the problem!

<h2>Question a :</h2>

1 + 3 + 5 + 7 + 9 + ... + 99

<em>initial term = a = 1</em>

<em>common difference = d = ( 3 - 1 ) = 2</em>

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$99 = 1 + (n-1)2$

$99-1 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

At last , we could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 1 + (50-1) \times 2 )$

$S_{50} = 25 ( 2 + 49 \times 2 )$

$S_{50} = 25 ( 2 + 98 )$

$S_{50} = 25 ( 100 )$

$\large { \boxed { S_{50} = 2500 } }$

<h2>Question b :</h2>

In this question let us find the series of even numbers first , such as :

2 + 4 + 6 + 8 + ... + 100

<em>initial term = a = 2</em>

<em>common difference = d = ( 4 - 2 ) = 2</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$100 = 2 + (n-1)2$

$100-2 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 2 + (50-1) \times 2 )$

$S_{50} = 25 ( 4 + 49 \times 2 )$

$S_{50} = 25 ( 4 + 98 )$

$S_{50} = 25 ( 102 )$

$\large { \boxed { S_{50} = 2550 } }$

At last , we could find the result of the series.

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100

= ( 1 + 3 + 5 + 7 + ... + 99 ) - ( 2 + 4 + 6 + 8 + ... + 100 )

= 2500 - 2550

= -50

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

<h2>Question c :</h2>

-100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50

<em>initial term = a = -100</em>

<em>common difference = d = ( -99 - (-100) ) = 1</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$50 = -100 + (n-1)1$

$50+100 = (n-1)$

$150 = (n-1)$

$n = 151$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{151} = \frac{1}{2}(151) ( 2 \times (-100) + (151-1) \times 1 )$

$S_{151} = 75.5 ( -200 + 150 )$

$S_{151} = 75.5 ( -50 )$

$\large { \boxed { S_{151} = -3775 } }$

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

3 0

3 years ago

Read 2 more answers

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners

jeyben [28]

Answer: The sample space showing the possible orders of the other three runners is

$S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}$

Step-by-step explanation:

Since we have given that

Number of runners = 4

Four runners are as follows:

Fran, Gloria, Haley, and Imani.

Since Haley is the first runner in the relay,

So, Sample space showing the possible order of the other three runners.

$S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}$

Hence, the sample space showing the possible orders of the other three runners is

$S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}$

8 0

4 years ago

Read 2 more answers

Charlie guesses that his dog weighs 34.5 lb. The dog actually weighs 32.7 lb.

In-s [12.5K]

Its simple The answer is 5.5%

5 0

4 years ago

A rectangle has a perimeter of 46 meters and a base of 8 meters. What is the height?

Igoryamba

Answer:

15 metres

Step-by-step explanation:

perimeter of rectangle = 2(base + height)

=2(8+h) = 46

= 16 + 2h = 46

= 2h = 46 - 16

= 2h = 30

= h = 15

15 metres is the height of rectangle

3 0

3 years ago