The accurate selections are: 1. For both families, the graph representing the connection between the number of pizzas (x) and the amount of slices (y) intersects at the origin (0, 0) and forms a straight line. 2. If the Wilson family orders 3 large pizzas from the same pizza shop as the Hernandez family, they will have a greater number of slices than the Hernandez family once the pizzas are sliced. The equations for the relationships between total slices (y) and pizzas ordered (x) are as follows: y = a × x, where 'a' indicates slices per pizza. For the Hernandez family, we have y = 24 when x = 3, resulting in a = 24/3 = 8 slices per pizza, producing the equation y = 8 × x. For the Wilson family, the relationship is represented by y = 10 × x. When both families’ equations are plotted, the result is straight-line graphs with a y-intercept of 0, meaning they pass through (0, 0). Thus, if the Wilsons order 3 large pizzas, they will have y = 10 × 3 = 30 slices, exceeding the Hernandez family's 24 slices.
9 / 16 + 1/2 =?
Step 1. To add fractions, they must share the same denominator. Here the denominators are 16 and 2. Since 16 is 8 times 2, multiply 1/2 by 8 to match denominators.
(1 * 8) / (2 * 8) = 8 / 16
Step 2. Add the numerators over the common denominator.
9/16 + 8/16 = (9+8) / 16 = 17 / 16
Step 3. Reduce the fraction if possible.
17/16 is already in simplest form. Therefore, 9/16 + 1/2 = 17/16
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) ± 
* 
]
[(82.3 - 81.2) ± 1.708 * (6.11 * 
]
[-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!
Greetings from MrBillDoesMath!
The answer is:
669/221
Discussion:
The ratio of 669 to 221 equals 669/221. Observing the factors, 669 is 3 * 223 and 221 is 13 * 17. As all these factors are distinct primes, nothing cancels in their ratio. Thus, 669/221 remains in its simplest form.
Answer:
The illustration provided shows the graph
Step-by-step explanation:
Let
x ------> number of times Emma cuts the grass
y ------> hours Emma spends babysitting
it is known that
------> represents the inequality of the scenario
The solution is the shaded region above the solid line where both x and y are positive
The equation for the solid line is represented as 
The slope of the line is negative 
The y-intercept is at the point 
(the y-value when x is zero)
The x-intercept is at 
(the x-value when y equals zero)
therefore
The illustration provided shows the graph
