Throw a cube once. Consider event A: "Number of dots greater than 3".
a) List the outcomes that belong to event A.
b) Formulate the complementary event Aˉ and list its outcomes.
Determine if the piecewise function f(x)={x2−4x+13,−12x−3,x≤−4x>−4 is differentiable, continuous, both, or neither at the point where the rule changes.
Houa, a salesperson, earned 135commissionon1700 total sales. The commissions were 9% on phone sales and 6% on computer sales. Write a system of equations to find the phone and computer sales amounts. Let x be the phone sales and y be the computer sales.
Then the system of equations is:
0.09x+0.06y=135x+y=1700
Solve the following equations for the given variable, showing work to isolate variable:
a. 0.3(2−3r)=2.1r+6
b. 11=3n+4
c. −712(3x−8)−4x=2−4(2x−3)
d. −4(2x−3)=6(4x−7)
Find the area A(x) of a rectangular field with 160 meters of fencing, where a side length is x meters. Determine the side length x that maximizes the area and the maximum area. (a) A(x)=x(160−2x)
(b) The side length x that maximizes the area is x=40 meters.
(c) The maximum area is A(40)=3200 square meters.
Estimate the proportion of first-time customers from a sample of 129 orders, given that 36% of orders come from first-time customers. Find the probability that the sample proportion is between 0.29 and 0.41.
Multiply 2-digit numbers: Bake sale muffins sold for $2 each, with 7 pans of 12 muffins from Eric and 6 pans from Pamela. How much can the school earn?
Find a 99% confidence interval for the true mean lifetime of a brand of light bulbs with a sample of 80 bulbs having a mean lifetime of 497 hours and a standard deviation of 45 hours. The lower and upper limits are 488.5 and 505.5 hours, respectively.
Zwei Kugeln werden mit Zurücklegen aus einer Urne mit 5 roten, 10 gelben, 7 blauen und 3 schwarzen Kugeln gezogen. Wie groß ist die Wahrscheinlichkeit, dass genau 2 blaue Kugeln gezogen werden? P=Gesamtanzahl der Mo¨glichkeitenAnzahl der Mo¨glichkeiten fu¨r genau 2 blaue Kugeln
The price of a computer component decreases by 13% per year. Is the decline linear or exponential? If the component costs $50 today, what will it cost in three years? Is the decline in price linear or exponential?
exponential What will the component cost in three years?
$38.83
Solve for the missing term in the given linear equation, simplifying fractions. 5s+8−6s=1+8=1−s=
Combine like terms
s=
Subtract 8 from both sides
Divide both sides by −1
What quality characterizes a linear function? A linear function has a constant slope because it has a constant rate of change and a straight-line graph.