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lora16 [44]
3 years ago
6

Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small

Mathematics
1 answer:
Kitty [74]3 years ago
7 0

Answer:

20 cups

Step-by-step explanation:

Let the small pitchers be given by s

and the larger pitchers by l

According to the given information:

2s + l = 8....(1) \\ and \\ l - s = 2 \\ l = s + 2...(2) \\ substituting \: l = s + 2 \: in \: equation \: (1) \\ 2s + s + 2 = 8 \\ 3s = 8 - 2 \\ 3s = 6 \\ s =  \frac{6}{3}  \\ \huge \red{ s = 2} \\ substituting \:   s  = 2 \: in \: equation \: (2)  \\ l = 2 + 2 \\ \huge \purple{ l = 4}\\\\Now\\ 3l +4s \\= 3\times 4+4\times 2\\= 12 +8\\= 20\: cups

So, 3 large pitchers and 4 small pitchers hold 20 cups of water.

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The cafeteria has 6 round tables and 23 rectangular chairs tables. If each round table has 7 chairs ,and each rectangular table
shtirl [24]

Answer:

456

Step-by-step explanation:

Number of chairs around the round tables = 6×7=42

Number of chairs around the rectangular tables =23×18=414

The total number of chairs in the cafeteria = 6×7+23×18=456

4 0
3 years ago
Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of
tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A                          Sample B

x_A = 30                              x_B = 50

n_A = 100                             n_B =250

Solving (a): Standard error using formula

First, calculate the proportion of A

p_A = \frac{x_A}{n_A}

p_A = \frac{30}{100}

p_A = 0.30

The proportion of B

p_B = \frac{x_B}{n_B}

p_B = \frac{50}{250}

p_B = 0.20

The standard error is:

SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}

SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}

SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}

SE_{p_A-p_B} = \sqrt{0.00274}

SE_{p_A-p_B} = 0.052

Solving (a): Standard error using bootstrapping.

Following the below steps.

  • Open Statkey
  • Under Randomization Hypothesis Tests, select Test for Difference in Proportions
  • Click on Edit data, enter the appropriate data
  • Click on ok to generate samples
  • Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A                          Sample B

x_A = 23                              x_B = 57

n_A = 100                             n_B =250

p_A = 0.230                          p_A = 0.228

So, we have:

SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}

SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}

SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}

SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}

SE_{p_A-p_B} = \sqrt{0.002475064}

SE_{p_A-p_B} = 0.050

5 0
2 years ago
How would I do this question.
olga2289 [7]

Answer:

The density of cube is 6.17959 \frac{g}{cm^{3} }

Step-by-step explanation:

The density is given by ration of a mass of body and volume occupied by a body.

\rho = \frac{m}{V}

Where,

\rho is density.

m is mass of a body

V is the volume of a body

Given that one side of the cube is 0.53cm

Hence, the volume of a body is V=0.53^{3}=0.148877cm^{3}

Now, the Density of the cube will be

\rho = \frac{m}{V}

\rho = \frac{0.92}{0.148877}

\rho =6.17959

Thus, The density of cube is 6.17959 \frac{g}{cm^{3} }

3 0
3 years ago
A submarine dives 320 feet below the water's surface. Over the next six
sergeinik [125]

Answer:

80

Explanation:

Since it rises at a rate of 40 feet per minute, just multiply 40 times 6 to get 240. Then subtract 320 minus 240 to get 80

3 0
2 years ago
How many questions will the equation 5(3x-9)=(6x+9) have
Delicious77 [7]
What do you mean?????????????
8 0
2 years ago
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