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Questions in mathematics

[Done] USING A PRIME FACTORIZATION Find the number represented by the prime factorization. 49. [tex]$2^2 \cdot 3^2 \cdot 5$[/tex] 50. [tex]$3^2 \cdot 5^2 \cdot 7$[/tex] 51. [tex]$2^3 \cdot 11^2 \cdot 13$[/tex]

[Done] The equation [tex]a=\frac{1}{2}\left(b_1+b_2\right) h[/tex] can be used to determine the area, [tex]a[/tex], of a trapezoid with height, [tex]h[/tex], and base lengths, [tex]b_1[/tex] and [tex]b_2[/tex]. Which are equivalent equations? Check all that apply. [tex]\frac{2 a}{h}-b_2=b_1[/tex] [tex]\frac{a}{2 h}-b_2=b_1[/tex] [tex]\frac{2 a-b_2}{h}=b_1[/tex] [tex]\frac{2 a}{b_1+b_2}=h[/tex] [tex]\frac{a}{2\left(b_1+b_2\right)}=h[/tex]

[Done] Consider the following function: [tex]f(x)=\left\{\begin{array}{ll} \frac{x^2-2 x-24}{x+4} & \text { if } x \neq-4 \\ -2 & \text { if } x=-4 \end{array}\right.[/tex] Determine if [tex]f(x)[/tex] is continuous at [tex]x=-4[/tex]. If not, select the option with the correct reasoning as to why not. A. Continuous at [tex]x=-4[/tex] B. Not continuous at [tex]x=-4[/tex] because [tex]\lim _{x \rightarrow-4} f(x) \neq f(-4)[/tex] C. Not continuous at [tex]x=-4[/tex] because [tex]\lim _{x \rightarrow-4} f(x)[/tex] does not exist D. Not continuous at [tex]x=-4[/tex] because [tex]f(-4)[/tex] is undefined

[Done] The table below shows the amount of carbohydrates in similar servings of different fruits. [tex]\begin{table}\captionsetup{labelformat=empty}\caption{Amount of Carbohydrates in Fruit}\begin{tabular}{|c|c|}\hline 287 mL of Frult & Cabohydrates (Grams) \\ \hline Apples & 17 \\ \hline Bananas & 34 \\ \hline Cherries & 19 \\ \hline Grapelruit & 24 \\ \hline Oranges & 21 \\ \hline Peaches & 16 \\ \hline Watermelons & 12 \\ \hline\end{tabular}\end{table}[/tex] If this data was placed in a bar graph, which statement would describe the graph? A. The graph would have only four bars shorter than the bar for grapefruits. B. The graph would have five bars taller than the bar for apples. C. The graph would have grapefruits and oranges as the tallest bars.

[Done] Solve the following equations: 1. [tex]2x-20+8x+40=180[/tex] 2. [tex]10x-1=8x+7[/tex] 3. [tex]6(x-2)-x-3[/tex] 4. [tex]5x+2(x-2)=45[/tex] 5. [tex]4x+5=4x+6[/tex] 6. [tex]6x+3=.10x+6[/tex] 7. [tex]2x-8+2(x-5)=360[/tex] 8. [tex]\frac{3}{5}x-12=\frac{8}{5}x+5[/tex]

[Done] Which statement is true considering a significance level of 5%? A. The result is not statistically significant, which implies that wearing a watch does not help people manage their time better. B. The result is statistically significant, which implies that wearing a watch helps people manage their time better. C. The result is statistically significant, which implies that wearing a watch does not help people manage their time better. D. The result is not statistically significant, which implies that this result could be due to random chance.

[Done] Select Yes or No to state whether each data set is likely to be normally distributed. | Data Set | Yes | No | | --------------------------------------------- | --- | -- | | the weights of the babies born at a hospital | | | | the number of babies born each month at a hospital | | | | the number of rooms on each floor of a hospital | | | | the lengths of the babies born at a hospital | | |

[Done] $\frac{6^{-4}}{6^{-4}}$

[Done] The ordered pairs in the table below represent a linear function. What is the slope of the function? A. [tex]$\frac{1}{4}$[/tex] B. [tex]$\frac{1}{2}$[/tex] C. 2 D. 4

[Done] Write each percent as a fraction or mixed number. Simplify. 1. 121% 2. 25% 3. 14% 4. 130% 5. 12 \frac{1}{2}%