All categories

3 years ago

3. A restaurant bill of $350 was paid using $5 notes and $50 notes. The total number of

Mathematics

1 answer:

Sonbull [250]3 years ago

3 0

The number of $5 notes is 10 and $50 notes is 6

Step-by-step explanation:

Let x be the number of $5 notes

and

y be the number of $50 notes

Then according to given statements

"The total number of notes used was 16."

x+y=16 Eqn 1

"A restaurant bill of $350 was paid using $5 notes and $50 notes."

5x+50y=350 Eqn 2

$From\ Eqn\ 1\\x+y=16\\y=16-x\\Putting\ y=16-x\ in\ equation\ 2\\5x+50(16-x)=350\\5x+800-50x=350\\-45x+800=350\\Subtracting\ 800\ from\ both\ sides\\-45x+800-800=350-800\\-45x=-450\\Dividing\ both\ sides\ by\ -45\\\frac{-45x}{-45}=\frac{-450}{45}\\x=10$

Putting x=10 in equation 1

$10+y=16\\y=16-10\\y=6$

So,

The number of $5 notes is 10 and $50 notes is 6

Keywords: Linear Equations, Variables

Learn more about linear equations at:

#LearnwithBrainly

You might be interested in

Please help please help please help please help please help please help

MrRa [10]

I think it’s the last one

4 0

3 years ago

A sample of 100 people is classified by gender (male/female) and by whether they are registered voters. The sample consists of 8

uysha [10]

Answer:

Step-by-step explanation:

Given :

Male Female Total

Registered 60

Non registered 40

Total 20 80

Solution :

N= 100

Formula of expected frequency = $E_{ij}=\frac{T_i \times T_j}{N}$

$E_{ij}$ = expected frequency for the ith row/jth columm.

$T_i$ = total in the ith row

$T_j$ = total in the jth column

N = table grand total.

So, using formula $E_{11}=\frac{T_1 \times T_1}{100}$

$E_{11}=\frac{60 \times 20}{100}$

$E_{11}=12$

$E_{12}=\frac{T_1 \times T_2}{100}$

$E_{12}=\frac{60 \times 80}{100}$

$E_{12}=48$

$E_{21}=\frac{T_2 \times T_1}{100}$

$E_{21}=\frac{40 \times 20}{100}$

$E_{21}=8$

$E_{22}=\frac{T_2 \times T_2}{100}$

$E_{22]=\frac{80 \times 40}{100}$

$E_{22}=32$

Expected frequency table

Male Female Total

Registered 12 48 60

Non registered 8 32 40

Total 20 80

So, the expected frequency for males who are registered voters are $E_{11}=12$

5 0

3 years ago

Which transformation will map an isosceles trapezoid onto itself? rotation by 180° about its center, reflection across a diagona

alukav5142 [94]

Answer:

The correct option is 4.

Step-by-step explanation:

The non parallel sides of an isosceles trapezoid are congruent.

The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if

1. Reflection across a line joining the midpoints of parallel sides.

2. Rotation by 360° about its center.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.

If we reflect the trapezoid across a diagonal, then the resultant figure will be a parallelogram.

If we reflect across a line joining the midpoints of the nonparallel sides, then the parallel sides will interchanged.

After rotation by 360° about the center, we always get an onto figure.

Therefore option 4 is correct.

6 0

3 years ago

Read 2 more answers

This week, Sarah spent a total of 120 minutes studying. This total was 20 more

MrMuchimi

Answer:

She spent 25 minutes studying last week

Step-by-step explanation:

L = last week

120 = 4L + 20

Subtract 20 from either side

100 = 4L

Divde either side by 4

25 = L

4 0

3 years ago

⦁ In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confiden

fomenos

Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = $\frac{354}{1219}$

n = sample of US adults = 1291

p = population proportion of adults

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

significance level are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ]

= [ $\frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ , $\frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ ]

= [0.265 , 0.316]

Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

5 0

3 years ago