Number 1.
Subtracting Negative Is The Same As Adding.
<span>So, It Would Be Equivalent To A
</span>Number 2:
Subtracting From A Negative Is Making The Negative Number Larger.
<span>So, It Would Be A
</span>Number 3:
<span>Positive Plus Positive Makes Larger Positive:
37 + 13 = 50</span>.
<span>So, 3 Is D.
Number 4:
</span>Adding Negative Is Making Positive Numbers Smaller.
So, It Is C.
Number 5:
This Is C, Because -30 + 30 = 0 + 1 = 1
Answer:
y = -3x + 6
Step-by-step explanation:
Slope-intercept form:
y = mx + b
m (slope) = 
or -3
b (y-intercept, or where the line crosses the y-axis) = 6
y = -3x + 6
<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
Answer:
H0: p = 0.078
Ha: p ≠ 0.078
Step-by-step explanation:
The researchers say that the rate is about 7.8%, or 0.078 as a decimal. That makes that the null hypothesis because using "is" in math is the same as saying "equals" and the null hypothesis always has the statement of equality in it. The reason there is a not equals to sign in the alternate is for this reason as well. The researchers say it is about that amount, not more or less than that amount. So it makes this a 2 tailed test. If the amount is significantly higher or lower, then we might have to reject the null hypothesis depending on the outcome of the test.
