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blondinia
2 months ago
7

The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x +

5y = 59→3x + 5y = 59 13x = 39Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?2x – y = –410x – 5y = –207x = 3913x = 39
Mathematics
1 answer:
babunello [11.8K]2 months ago
6 0
2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39..... this is derived from adding the two equations on the right.

13x = 39 can be used in place of 3x + 5y = 59 in the initial system and will yield the same result.
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One of your peers claims that boys do better in math classes than girls. Together you run two independent simple random samples
babunello [11817]

Answer:

Step-by-step explanation:

Hello!

To determine whether boys excel in math classes compared to girls, two random samples were collected:

Sample 1

X₁: score achieved by a boy in calculus

n₁= 15

X[bar]₁= 82.3%

S₁= 5.6%

Sample 2

X₂: score obtained by a girl in calculus

n₂= 12

X[bar]₂= 81.2%

S₂= 6.7%

To estimate a confidence interval for the difference between the average percentages of boys and girls in calculus, it's essential that both variables come from normally distributed populations.

For utilizing a pooled variance t-test, it is also required that the population variances, though unknown, are assumed to be equal.

The confidence interval can then be calculated with:

[(X[bar]_1 - X[bar]₂) ± t_{n_1+n_2-2;1-\alpha /2} * Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }]

Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*(5.6^2)+11*(6.7^2)}{15+12-2} }= 6.108= 6.11

t_{n_1+n_2-2;1-\alpha /2}= t_{15+12-2;1-0.05}= t_{25;0.95}= 1.708

[(82.3 - 81.2) ± 1.708 * (6.11 * \sqrt{\frac{1}{15}+\frac{1}{12} }]

[-2.94; 5.14]

Using a 90% confidence level, the interval [-2.94; 5.14] is expected to encompass the true difference between the average percentages achieved by boys and girls in calculus.

I hope this is of assistance!

3 0
2 months ago
Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. Circles F and J are congruent. Line segments F E and F D are radii. A line c
Zina [12379]

Answer:

The measure of arc GH is 80 degrees.mGH=80^\circ

Step-by-step explanation:

Circles F and J are congruent.

\angle DFE \cong \angle GJH

Given that: m∠DFE = 80°

Angle DFE serves as the central angle of circle F.

Arc GH's measurement corresponds with the central angle from Circle J.

Since the two circles are congruent

mGH=\angle DFE = 80^\circ

The measure of arc GH, therefore, is 80 degrees.

8 0
2 months ago
Read 2 more answers
El perímetro de un rectángulo es 28cm, uno de los lados es 6cm más que el otro lado. Hallar el mayor lado del rectángulo.
Inessa [12570]

Answer: El lado mayor del rectángulo mide 10cm

Step-by-step explanation:

El perímetro de un rectángulo está dado por:

P = 2*L + 2*A

Donde L es la longitud y A es el ancho.

Como sabemos que un lado es 6cm más largo que el otro, podemos expresar esto como:

L = A + 6cm.

Por lo tanto, P = 28cm = 2*L + 2*A

Sustituyendo la primera ecuación en la segunda tenemos:

28cm = 2*(A + 6cm) + 2*A

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4cm = A.

Así que el ancho es 4 cm y la longitud se calcula como L = 4cm + 6cm = 10cm

4 0
3 months ago
What kind of vehicle do you prefer: two-door, four-door or minivan? What type(s) of data will this statistical question represen
PIT_PIT [12445]
I believe it’s numerical data
3 0
1 month ago
Read 2 more answers
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Svet_ta [12734]

Answer:

$82.3

Step-by-step explanation:

82 multiplied by 25 equals 2050.

Adding 90 gives 2140.

Dividing 2140 by 26 results in 82.3.

5 0
2 months ago
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